WASHINGTON — A bill to limit the cost of insulin to $35 a month for most Americans who depend on it passed the House on Thursday, raising Democrats’ hopes that the party could take at least one step toward fulfilling its promise of lowering drug costs.

The bill attracted unanimous support from Democrats who voted, as well as from 12 Republicans, making it a rare piece of bipartisan policy legislation.

To become law, the bill will need to attract at least 10 Republican votes in the Senate to overcome a filibuster. Some lawmakers involved in the effort have expressed optimism that such a coalition might be possible, but few Republican senators have publicly endorsed the bill yet. Senator Susan Collins, Republican of Maine, has been working with Senator Jeanne Shaheen, Democrat of New Hampshire, on a broader bill related to insulin prices.

The bill would have substantial benefits for many of the nearly 30 million Americans who live with diabetes. Insulin, a lifesaving drug that is typically taken daily, has grown increasingly expensive in recent years, and many diabetes patients ration their medicines or discontinue them because of the cost. About one in five Americans who take insulin would save money under the proposal, according to a recent analysis from the Kaiser Family Foundation.

But the insulin bill represents a substantial scaling back of Democratic ambitions to tackle high drug prices for all Americans. A broader prescription drug package, written as part of the $2.2 trillion social spending and climate bill that has stalled in the Senate, would limit price increases on all prescription drugs, improve the generosity of Medicare’s drug coverage, and allow the government to negotiate directly on the price of some drugs used by Medicare patients, while also limiting insulin co-payments.

Other parts of the broader bill would expand health insurance coverage, extending insulin coverage to diabetes patients who are uninsured. The bill that passed the House on Thursday would not improve the affordability of insulin for people who lack health insurance.

The insulin bill may be the Democrats’ best chance of passing part of their popular prescription drug agenda, as the future of the larger package remains unclear.

“If the effort to address drug prices ends with this plan to cap out-of-pocket costs for insulin, it will amount to crumbs compared to Democrats’ initial ambitions to allow the government to negotiate drug prices,” said Larry Levitt, the executive vice president for health policy at the Kaiser Family Foundation, a health research group.

On the House floor, several Republicans expressed their opposition to the measure.

“We all share the goal of reducing the cost of insulin,” said Representative Cathy McMorris Rodgers of Washington, the top Republican on the House Energy and Commerce Committee. “This bill, however, is not the right answer.”

The pharmaceutical industry opposed the drug price regulations in the social spending and climate legislation, but it has not vocally opposed the insulin bill. While the bill would lower costs for many individual patients who take insulin, it would do nothing to reduce the prices paid to the companies that make it. Instead, insurance companies would simply pay a larger share of the price. The Congressional Budget Office estimated that the bill would increase government spending, since health insurers, including Medicare, would be responsible for a greater share of insulin costs.

But consumer insulin costs have emerged as a politically potent problem, given how widespread diabetes is in the United States, and one that is relatively easier to solve than the prices for prescription drugs overall. At a White House event in December, President Biden centered a speech about prescription drugs around the cost of insulin.

“I think it’s safe to say that all of us, all of us, whatever our background, our age, where we live, we can agree that prescription drugs are outrageously expensive in this country,” Mr. Biden said at the event, where patients with diabetes told their stories of struggles to afford the medicine.

Debate on the broader legislation has slowed, but has not died. Senator Joe Manchin III, Democrat of West Virginia and a key centrist holdout, has expressed support for the prescription drug provisions in the bill, even as he has been more skeptical about other parts of the package.

At her weekly news conference on Thursday, Speaker Nancy Pelosi of California tried to cast the passage of the insulin bill as progress toward the party’s broader drug-pricing agenda. She described insulin prices as a “kitchen-table issue.”

“It is for us a step in the direction of the secretary being able to negotiate for lower drug prices beyond insulin,” she added, referring to the secretary of the Department of Health and Human Services.

Senator Patty Murray, Democrat of Washington and the chairwoman of the Senate’s Health, Education, Labor and Pensions Committee, is a co-sponsor of similar insulin legislation in her chamber. She said she remained committed to passing a full suite of prescription drug price reforms, but that she viewed the insulin issue as particularly urgent.

“We’re focused on insulin, because it affects so many Americans in so many specific ways,” she said.

Emily Cochrane contributed reporting.