WASHINGTON — As Senator Bernie Sanders, the Vermont independent, prepares to take control of the Senate Budget Committee, he is mounting an aggressive campaign ahead of what will be one of his first tests as chairman: securing the support needed to increase the federal minimum wage to $15 an hour by 2025 in a pandemic relief package.

Whether he succeeds will not only affect the jobs and wages of millions of American workers, but also help define the limits of Democrats’ willingness and ability to use procedural maneuvers to shepherd major policy proposals past entrenched Republican opposition in an evenly divided Senate.

President Biden and top Democratic leaders have repeatedly said their first choice is to pass Mr. Biden’s sweeping $1.9 trillion stimulus proposal with bipartisan support. But Republicans are already balking at the scope of the proposal, and raising the minimum wage to $15 is a particularly contentious part of the bill, a progressive priority that draws intense opposition from many Republicans.

So Democrats are barreling toward using a fast-track process known as budget reconciliation to avoid the 60-vote threshold typically needed to overcome a filibuster and approve legislation. That would allow them to pass the measure with no Republican support and Vice President Kamala Harris casting the tiebreaking vote. Both chambers are expected to vote on a budget resolution — a measure that will formally direct committees in the House and the Senate to begin drafting the relief package, kicking off the reconciliation process — in the coming days.

Mr. Sanders argued in an interview that Democrats clinched control of the White House and the Senate in part by promising sweeping policy changes and additional pandemic relief, and that not supporting the full legislation would betray their voters and undermine faith in the party’s governing.

“If that is the case, if that is what we do, we will surely be a minority in two years,” Mr. Sanders said. “We have to keep the promises that we made.”

But Republicans have said that failing to compromise would jeopardize future bipartisan negotiations for a president who has repeatedly called for unity, with a group of 10 Republican senators moving to unveil their own $600 billion proposal as early as Monday in an effort to negotiate with the administration.

And the minimum wage poses a particularly polarizing test: Including it in the package would be an aggressive use of reconciliation, one some lawmakers fear will not be allowed by the Senate parliamentarian. That could force Democrats into even more contentious tactics if they want the minimum wage to pass, setting up a battle between a priority championed by liberals like Mr. Sanders and the further fraying of Senate norms.

“Minimum wage is probably the most controversial of those proposals,” Mr. Sanders acknowledged. “I’m sure every Democratic senator will have some problem with some aspect of reconciliation, I do, others do — I am absolutely confident that people will support our new president and do everything we can to help the working families of this country.”

Other lawmakers, including some Republicans, have argued that the pandemic relief package should be scaled down, with items like the minimum wage provision left for another legislative battle later in the year. Most House Republicans voted against a stand-alone minimum wage bill in 2019, pointing to a Congressional Budget Office report that estimated the provision would put an estimated 1.3 million Americans out of work. Senate Republicans, in control of the chamber, did not take it up.

“That’s an agenda item for the administration, so be it,” Senator Lisa Murkowski, Republican of Alaska, told reporters. “Should it be included as part of a Covid relief package? I think it takes the focus off the priority, which is what is the immediate need today.”

“Hey,” she added, “you get the keys to the car now. And so let’s get some legislation done, but you don’t need to think that you need to get it all in one package.”

Senator Lindsey Graham, Republican of South Carolina, bluntly told reporters in January that “we’re not going to do a $15 minimum wage in it” and that Mr. Biden was better off reaching out to Capitol Hill and negotiating a compromise.

Mr. Sanders and Democrats have argued that with jobless benefits set to begin expiring in mid-March, there is little time to win over their Republican counterparts, who embarked on similar reconciliation efforts in 2017 to repeal portions of the Affordable Care Act and pass a sweeping tax overhaul.

But to secure the first increase in the federal minimum wage since 2009, even under reconciliation Mr. Sanders and liberal Democrats can afford to lose little, if any, support from the rest of the caucus.

Several lawmakers, including Representative John Yarmuth of Kentucky, the chairman of the House Budget Committee, have voiced skepticism that the minimum wage provision can prevail through the rules of the reconciliation process, which imposes strict parameters to prevent the process from being abused. Under the so-called Byrd Rule, Democrats cannot include any measure that affects the Social Security program, increases the deficit after a certain period of time set in the budget resolution or does not change revenues or spending.

The decision on whether the provision can be included in the reconciliation package lies with the Senate parliamentarian. Ms. Harris could ultimately overrule the parliamentarian — something that has not been done since 1975 — and Mr. Sanders declined to say whether a rejection of the minimum wage provision would prompt Democrats to do so.

“Our first task is to get the ruling of the parliamentarian,” he said. “That’s what I would like to see and that’s what we are focused on right now.”

Some Democrats, including Mr. Yarmuth, have signed on instead to stand-alone legislation for the minimum wage increase as another avenue for approval, but one that would require Republican support. Cedric Richmond, a top White House adviser, argued that “the minimum wage has been expanded or increased during times of crisis before” but declined to say whether it should be part of the coronavirus package or a stand-alone bill.

Mr. Sanders pointed to two new studies, shown to The New York Times ahead of their publication, that argue that the minimum wage would have a direct impact on the federal budget, opening a door to using reconciliation. In a new paper, Michael Reich, a professor of economics and labor economist at the University of California, Berkeley, estimated that approval of the minimum wage would have a positive effect of $65.4 billion per year largely because of increases to payroll and income tax revenue.

“It seems to me that it has pretty substantial budgetary impacts,” Mr. Reich, who has long studied the effects of minimum wage, said of the provision in an interview, adding that he had been conservative in his estimate.

Another report, produced by three economists at the Economic Policy Institute, a liberal think tank and a longtime advocate for increasing the minimum wage, found that there would be “significant and direct effects” on the federal budget by increasing payroll tax revenue by $7 billion to $13.9 billion and reducing expenditures on public assistance programs by $13.4 billion to $31 billion.

“This is a sizable chunk of money, no matter how you look at it,” said David Cooper, who wrote the report with Ben Zipperer and Josh Bivens. They determined that increased revenue would prevent many workers and their families from qualifying for assistance programs, reducing expenses.

But it remains uncertain whether that evidence will be enough to clear the parameters of the Byrd Rule, given that those effects could be ruled “merely incidental.” The Congressional Budget Office, one of the arbiters of the budget effects, found during the last Congress that there would be minimal impact based on the wages of some federal employees.

But Mr. Sanders, pressed on whether Democrats had the votes in an evenly divided Senate to move forward with the minimum wage provision, declared that there were “50 votes to pass reconciliation, including minimum wage, yes.”

“In totality, what Democrats are saying,” he said, is “we’ve got to support the president, we’ve got to address the crises facing working families and we’re going to pass reconciliation.”

Jim Tankersley and Chris Cameron contributed reporting.