WASHINGTON — The Senate on Thursday overwhelmingly approved a $35 billion measure to clean up the nation’s water systems, offering a brief moment of bipartisan cooperation amid deep divisions between the two parties over President Biden’s much larger ambitions for a multitrillion-dollar infrastructure package.

Republicans and Democrats alike hailed passage of the bill on an 89-to-2 vote as evidence that bipartisan compromise is possible on infrastructure initiatives, but lawmakers in both parties suggested that the spirit of deal-making could be fleeting.

Mr. Biden and Democratic leaders have said they want Republican support for a broad infrastructure package that aims to improve the nation’s aging public works system and address economic and racial inequities, after pushing a nearly $1.9 trillion pandemic relief bill into law with just Democratic votes. But Republicans have panned those proposals, which are to be financed with tax increases on high earners and corporations, and Democrats have said they may have to move them unilaterally if no compromise can be reached.

“We’re trying to work in a bipartisan way whenever we can — and this bill is a classic example,” Senator Chuck Schumer of New York, the majority leader, said of the water bill. “It doesn’t mean that we’ll be able to do the whole thing bipartisan, but we’ll do as much as we can.”

The legislation approved on Thursday would authorize funding to shore up the nation’s water systems, particularly in rural and tribal communities that have long been neglected and suffer from poor sanitation and unclean drinking water. A House Democratic aide, speaking on the condition of anonymity, said House committees had their own substantial proposals and looked forward to negotiations.

“I don’t want to overplay it, but I think it’s definitely a major positive,” Senator Shelley Moore Capito, Republican of West Virginia, said of the lopsided vote on the water infrastructure bill, which she helped spearhead. Yet Ms. Capito cautioned that the moment of cooperation might not last long if negotiations faltered.

Republicans have “made it clear that we don’t see the definition of infrastructure — physical core infrastructure — the same way” that Mr. Biden does, she said.

In his speech before a joint session on Congress on Wednesday, Mr. Biden applauded an infrastructure counteroffer put forward by Senate Republicans and called on lawmakers to “get to work.” Ms. Capito and other Republicans have been in touch with the White House over their $568 billion framework for roads, bridges, airports, ports and broadband.

But that plan, which Republicans have said is the largest infrastructure proposal they have offered, is a fraction of the spending Mr. Biden outlined, even before he unveiled a $1.8 trillion plan for investing in workers, child care and schools on Wednesday. It notably excluded all of Mr. Biden’s suggestions for how to pay for the spending — including tax increases on corporations — and did not provide clear alternatives.

It remains unclear whether Democrats will agree to winnowing down the scope of the economic platform or plans to pay for it by undoing key elements of the 2017 tax plan in order to win a handful of Republican votes. Some Democrats, including Senator Joe Manchin III of West Virginia, a key moderate, have urged their colleagues to negotiate with Republicans.

“I think there is a good reason for us to proceed with sincere bipartisan negotiations in the next few weeks — not indefinitely,” Senator Chris Coons, Democrat of Delaware, told reporters on Thursday. He said that making the attempt would be crucial for getting the requisite 50 Democratic votes to pass something unilaterally if those talks stalled.

Senator Rob Portman, Republican of Ohio, said he was optimistic, after conversations with Mr. Biden and White House staff members, that Senate Republicans and the administration could hatch a deal around a “narrower” definition of infrastructure, leaving other liberal proposals in Mr. Biden’s plans for a separate bill.

“I don’t know where the White House ends up on it,” Mr. Portman said. “The president last night said the right things, both in his speech and private conversations. I think they want to do an infrastructure package. They also want to do the other things. They understand that they don’t work together.”

Republican leaders, however, were more skeptical. Senator Mitch McConnell of Kentucky, the minority leader, said on Thursday that Mr. Biden had rattled off a “multitrillion-dollar shopping list that was neither designed nor intended to earn bipartisan buy-in.”

With the nearly $1.9 trillion stimulus plan still popular with a majority of voters, some Democrats are eager to wield their slim majorities in both chambers to push as many liberal priorities into law as possible.

Senator Bernie Sanders, the Vermont independent who is the chairman of the Budget Committee, said he and his panel had begun work on a budget resolution, legislation needed to unlock the reconciliation process that would allow them to circumvent a filibuster and push through a fiscal package without Republican votes. (Democrats have not yet committed to using the maneuver.)

“The calculus is, we get a lot more than we would if we chase our tail around and hope for this bipartisan mirage that is just over the horizon and keeps moving over the horizon,” said Senator Richard Blumenthal, Democrat of Connecticut.

Using reconciliation, Mr. Blumenthal acknowledged, could curtail certain provisions because of the strict rules that govern the process, and would not allow for any defections in the Senate. Even before Democrats try to muscle any legislation through that gantlet of parliamentary restrictions, they would have to ensure that the entire caucus in both chambers was united behind the contents.

That prospect already appears charged, with several Democrats cautioning reporters in recent days that Congress, not Mr. Biden, is ultimately responsible for shaping the fine details of any legislative plan. Some Democrats are pushing to make certain provisions permanent, including an expanded monthly benefit to families with children that Mr. Biden has suggested extending through 2025.

Other Democrats are advocating additional changes to the tax code, while several progressive lawmakers, including Mr. Sanders, are pushing to expand Medicare and include provisions to help lower the cost of prescription drugs.

“What is going to happen is there is going to be a major, major piece of legislation that is going to go a long way to improving life for the American people,” Mr. Sanders said. “All of us are going to have to take a deep breath and understand that we have to go forward right now to address the crises facing the country even if the bill is not 100 percent of what we want.”

Nicholas Fandos contributed reporting.