WASHINGTON — A congressional year that began with an assault on the seat of democracy ended at 4 a.m. Saturday with the failure of a narrow Democratic majority to deliver on its most cherished promises, leaving lawmakers in both parties wondering if the legislative branch can be rehabilitated without major changes to its rules of operations.

“It has been a horrible year, hasn’t it?” asked Senator Lisa Murkowski, Republican of Alaska, as she looked back on failed efforts to convict a former president and to create a bipartisan commission to examine the Jan. 6 attack on the Capitol, as well as numerous legislative endeavors that could not find bipartisan majorities.

The Senate limped out of town in pre-dawn darkness after slogging through nominations one by one, but leaving dozens of Mr. Biden’s nominees still awaiting confirmation to fill key positions at home and abroad — because a handful of Republican senators erected a blockade.

President Biden and Democrats can point to some major successes in 2021, including a $1.9 trillion pandemic aid plan that included a $300-per-child income support that slashed poverty rates; a $1.2 trillion bipartisan infrastructure law that had eluded the two previous presidents; the confirmation of 40 judges in Mr. Biden’s first year, the most of any president since Ronald Reagan; and a House inquiry that has begun to reveal more about the roots of the Jan. 6 riot.

But the desultory end to the first session of the 117th Congress left few happy. Republicans — helped along by Democratic holdouts — succeeded in obstructing much of Mr. Biden’s agenda, including a major voting rights push meant to neutralize new restrictions their party has enacted at the state level. Democrats accused them of an assault on the foundations of democratic pluralism.

At times, Democrats tried resorting to bare-knuckled tactics to steer around that obstruction — drawing charges from Republicans that they were trampling the rights of the congressional minority in ways that they would soon regret — and still fell short of their goals.

House Democrats, who hold a slim majority in their chamber, fumed at their counterparts in the evenly divided Senate for failing them, while Senate Democrats railed against two of their own — Senators Joe Manchin III of West Virginia and Kyrsten Sinema of Arizona — for grinding Mr. Biden’s agenda to a halt with their refusals to fall in line.

The disappointments were impossible to deny. Democrats have been warning with growing urgency that forces loyal to former President Donald J. Trump have been moving the pieces into place to disrupt or potentially overturn the next presidential election — through new barriers to voting, partisan election controls and gerrymandered House districts. Yet efforts to enact expanded voting rights, institute fair election rules or place any new controls on the presidency have hit a wall in the Senate.

A self-imposed Christmas deadline to pass a $2 trillion social safety net and climate change bill through the Senate came and went, with one senator in particular, Mr. Manchin, looking increasingly intransigent.

Other promises to overhaul the nation’s crippled immigration laws, force the conversion of electric utilities to renewable energy, strengthen gun safety laws and reform policing rules appear dead.

Even raising the borrowing limit to make sure the federal government did not default on debt incurred under both Mr. Trump and Mr. Biden could only be accomplished by the most convoluted of legislative machinations.

“Welcome to the United States Senate. I’ve been here for 25 years and I’ve seen the decline of this institution to the point where we no longer function as we once did,” said Senator Richard J. Durbin of Illinois, the No. 2 Democrat. He added, “Until we change the rules of the Senate and get serious about legislating on behalf of the American people, we’re going to continue to suffer this frustration.”

Lawmakers from both parties blamed their opponents for the malaise hanging over the Capitol. Senator Mitt Romney, Republican of Utah, said any number of issues might have been resolved — as the infrastructure issue was — if Democrats had simply approached open-minded Republicans to find solutions.

He pointed to an income security plan he rolled out in February that could have been the basis for negotiations as the Democrats struggled to extend their $300 child credit beyond 2021. No one even broached the subject with him, he said.

Liberal lawmakers bristled at the accusation, given the Republican Party’s refusal to recognize the grave threat to democracy that Mr. Trump represents through his lies about a “stolen” election and the manipulations of the party ahead of the next elections. Senator Elizabeth Warren, Democrat of Massachusetts, said her party had “openly begged Republicans to join us in crafting a voting rights bill that we could all support, and they have consistently refused.”

Senator Bernie Sanders, independent of Vermont, scoffed at the notion that Republicans would have helped address climate change, raise taxes on the wealthiest Americans and lower prescription drug prices — if they were only asked.

“I don’t think it’s fair to lay the blame on Congress,” he said. “I think this is what Republican extremism is all about.”

But beyond partisan finger pointing, few could argue the legislative branch of government was functioning properly. As long as most policy bills need 60 votes to overcome a Senate filibuster, Speaker Nancy Pelosi’s remarkable ability to corral her whisper-thin House majority will be for naught on most legislation. Though virtually all Senate Democrats are ready to change the filibuster rules, at least for some issues, like voting rights, they need unanimity — and Mr. Manchin and Ms. Sinema aren’t giving it.

Even where the filibuster is not a hindrance, Senate operations are dysfunctional. Democrats ended the filibuster on executive branch confirmations, yet a single senator, Ted Cruz, slowed confirmations of key national security officials to a crawl over his demand for a vote on sanctions over a Russian-backed gas pipeline. He then blamed the majority leader, Senator Chuck Schumer of New York, for failing to acquiesce.

“If Chuck Schumer wants to kill Biden’s nominees, he can do that,” Mr. Cruz, a Texas Republican, said. “It’s not clear to me why it’s in his interest to do that.”

And some of Mr. Biden’s nominees tasked with addressing supply chain issues gumming up global commerce remained blocked by Senator Rick Scott, Republican of Florida, who is demanding the commerce and transportation secretaries testify to Congress on those supply chain issues first.

“It’s ridiculous that we’re in this position,” fumed Senator Maria Cantwell, Democrat of Washington and the chairwoman of the Commerce, Science and Transportation Committee.

In the House, two Republicans, Representatives Marjorie Taylor Greene of Georgia and Paul Gosar of Arizona, were stripped of their committee assignments for social media posts that contained threats of violence against Democratic colleagues — and a third, Representative Lauren Boebert of Colorado, could yet be sanctioned for suggesting one of two Muslim women in the House, Representative Ilhan Omar, Democrat of Minnesota, could be a suicide bomber. When the House on Tuesday debated Ms. Omar’s bill to create a State Department post to combat anti-Muslim bigotry, Representative Scott Perry, Republican of Pennsylvania, accused Ms. Omar of harboring terrorist sympathies.

Insults and shout-downs have become the order of the day. Ms. Taylor Greene showed up in September at a Democratic news event to heckle the majority party, calling them baby killers. In July, liberal protesters drowned out her and other far-right House members with jeers and taunts as they tried to hold a media event denouncing the treatment of those imprisoned for the attack on the Capitol.

Indeed, the ill will on Capitol Hill cannot be separated from the Jan. 6 attack — and the fallout from it — a hasty impeachment of Mr. Trump that ended in acquittal and an attempted convening of a bipartisan commission to examine the attack that ended with a Republican filibuster in the Senate.

Norman J. Ornstein, an emeritus scholar at the American Enterprise Institute, a conservative think tank, tagged Congress as “the broken branch” back in 2006. But 2021, he said, started “with not just a broken branch but a broken Capitol.”

Senate Republicans had the chance in February to bar Mr. Trump from ever running for office by joining Democrats in convicting him of inciting an insurrection. While seven Republicans did vote to convict, the Senate needed 10 more.

Ms. Murkowski said that the revelations since those events — that some House Republicans encouraged the overturning of Mr. Biden’s victory, that Fox News personalities begged that Mr. Trump call off the riot and that the former president embraced an illegal, step-by-step effort to maintain control — further validated her votes to convict Mr. Trump and create an independent inquiry.

“On the Republican side, there was such an effort — we’ve got to get this behind us; we’ve got to get beyond it — and in fairness, we have work to do every day,” she said. “But this was not just a bad disagreement over policy. This was this was an insurrection. This was a threat to our very democracy.”

Other Republicans do not seem interested in learning any more about the riot. On Monday, Senator Josh Hawley, the junior Republican from Missouri who openly encouraged the rioters as they approached the Capitol, refused to discuss it further. “I’ve commented ad nauseam,” he said.

The impact of that attitude on the rest of Congress’s workings cannot be overstated, Mr. Ornstein said. Congress has gone from a maddening institution hampered by intentional checks and balances to one that is driven by a quest for partisan power, he said, pointing to Republican efforts to cover up the roots of Jan. 6, and their refusal to punish members who threaten violence, or even acknowledge members’ efforts to overturn the results of a lawful election.

“We don’t have two parties anymore. We have a party and a cult, and in a cult, the fear of being excommunicated or shunned is overwhelming,” he said. “That’s affected the behavior of large numbers of members.”

Republicans have their own beefs. Democrats have barely opened legislation to the kind of amendment processes that once produced bipartisan bills. House Democrats have not considered a single bill under a wide-open amendment process. Under strict controls, Republicans submitted 1,995 amendments for consideration. Democratic leaders allowed votes on only 275 of them.

Emily Cochrane contributed reporting.