WASHINGTON — Democrats’ $2.2 trillion social safety net, climate and tax bill faced new setbacks on Thursday as President Biden conceded that the measure was stalled for the moment and a top Senate official ruled that a section granting legal status for millions of undocumented immigrants — a top Democratic priority — must be dropped from the bill.

The decision by Senate parliamentarian was just the latest in a series of blows to the measure that have left Democrats frustrated and resigned to falling short of their goal of passing the legislation before the end of the year. It was the third time the chamber’s top rules enforcer had rejected a bid by Democrats to use the social policy bill to salvage their hopes of enacting an immigration overhaul, including legalizing large numbers of undocumented people.

Senator Richard J. Durbin of Illinois, the No. 2 Senate Democrat who for years has tried to provide a path to citizenship for the young immigrants known as Dreamers, said he was “disappointed and considering what options remain.”

“We’re not going to stop fighting for them,” Mr. Durbin said.

It came as Mr. Biden issued a lengthy statement noting that he had so far failed to reach agreement with Senator Joe Manchin III of West Virginia, a crucial Democratic holdout, on the broader package, and foreshadowing a rocky — and potentially lengthy — road ahead to finalize the bill and shepherd it into law.

“I believe that we will bridge our differences and advance the Build Back Better plan, even in the face of fierce Republican opposition,” Mr. Biden said. “It takes time to finalize these agreements, prepare the legislative changes and finish all the parliamentary and procedural steps needed to enable a Senate vote.”

He said that the work would continue “over the days and weeks ahead,” and that talks with Mr. Manchin would continue.

He did not mention the ruling, which was released just minutes before he issued the statement, but vowed to see the bill enacted into law.

Despite unanimous Republican opposition, Democrats had hoped to muscle the measure through the evenly divided Senate by Christmas, using the fast-track budget reconciliation process, which shields fiscal legislation from a filibuster.

But doing so would require the vote of every Democratic senator, making Mr. Manchin’s objections fatal. And it must also adhere to strict rules governing reconciliation, which require that every provision have a direct effect on the federal budget.

The parliamentarian has repeatedly ruled that the immigration provisions do not.

“The proposed parole policy is not much different in its effect than the previous proposals we have considered,” the parliamentarian wrote, according to a copy of her decision obtained by The New York Times. “These are substantial policy changes with lasting effects just like those we previously considered and outweigh the budgetary impact.”