Lawmakers are accelerating their push to extend the time frame for small-business owners to spend funds received through the $670 billion Paycheck Protection Program.

The Senate will consider legislation that would double, to 16 weeks, the amount of time businesses have to spend PPP loans. Backers say the proposal has bipartisan support.

Under the current rule, the earliest recipients of PPP funds must finish using them by May 29.

Congressional staffers say House Democrats are expected next week to bring to the floor a bill to change the program’s time frame—a step that they originally sought to include in the $3 trillion stimulus bill the House passed last week.

The program requires businesses to put 75% of its funding toward keeping workers on the payroll for the loan to be forgiven, and to do so within eight weeks. But that has proven difficult for many businesses—such as restaurants and hair salons—that have remained closed and have little or no work to offer employees.

Treasury Secretary Steven Mnuchin said in a virtual event Thursday that he supports extending the eight-week period but that congressional action is required to do so.

But he defended the requirement that recipients use 75% of the money on payroll costs, rather than rent or bills. Companies struggling to meet additional overhead costs, he said, can apply for other loans through the Small Business Administration.

“It’s called the Paycheck Protection Program. It’s not called the overhead protection program,” Mr. Mnuchin said. “We want most of this money to go to workers, and we believe that the 75% was exactly consistent with the way the program was designed.”

Mr. Mnuchin also expressed reluctance to disclose PPP funding that is extended to privately held companies. A number of public companies have disclosed receiving funds that they then had to return to the government following a public outcry.

“I think in the PPP it does not require disclosure,” he said, referring to private companies that receive money. “There is proprietary information because it’s tied off of payroll...that should not be in the public domain.”

Demand for the program has cooled considerably in recent weeks, with new funds approved at a rate of roughly $1 billion a day. According to SBA data, a total of $513 billion had been approved under the program by Tuesday, leaving about $130 billion still available after accounting for lender fees. The government pays fees to banks for issuing the PPP loans, which are guaranteed 100% by the government.

An SBA spokesman said funds returned by some lenders have been added back to the pool, bolstering availability. He didn’t disclose the amount of returned funds, but there is a gap of roughly $24 billion between the agency’s earlier loan-approval data and the latest accounting. The spokesman said the latest number reflects cancellations of duplicative loans, loans that didn’t close for whatever reason and loans that have been paid off.

Sen. Marco Rubio (R., Fla.), chairman of the Senate small-business panel,  said in a video posted Wednesday on Twitter that Senate Republicans are pushing to pass a stand-alone bill this week to extend the duration of a PPP loan from the current eight weeks to up to 16 weeks, adding such a bill “would probably get 99 or 98 votes” in the Senate.

“We are going to change PPP so that if you got a PPP loan, you have 12 or 14 or 16 weeks to spend the money on payroll,” Mr. Rubio said. “Still the same purpose, just some more flexibility because the crisis has changed.”

Sen. Ben Cardin of Maryland, the top Democrat on the small-business panel, has also called for extending the loan period and said he was working with Mr. Rubio on a legislative fix.

Separately, Sens. Michael Bennet (D., Colo.) and Todd Young (R., Ind.) will roll out on Thursday a bill calling for the extension to 16 weeks, as well as establishing a new loan program to help hard-hit small and medium-size businesses beyond the scheduled June 30 end of the current program, Senate aides say.

In the House, Rep. Dean Phillips (D., Minn.) and Rep. Chip Roy (R., Texas) have introduced a bill to adjust the Paycheck Protection Program, including extending the loan period and eliminating the requirement to use 75% of funds on payroll expenses.

Mr. Phillips said in a statement that he has “secured from Congressional leadership a commitment for a vote,” which is expected to take place next week. The bill’s measures were part of the House Democrat’s broader stimulus package passed last week, but were separated out to avoid getting caught up in political wrangling.

Mr. Phillips said in an interview that he had asked House Speaker Nancy Pelosi (D., Calif.) to bring the bill for a vote, while expressing disappointment in the House’s latest coronavirus response bill. She agreed to do so, and he voted for the bill, which had only Democratic support.

“It has a sense of urgency about it,” Rep. Pelosi said of Mr. Phillips’s proposal in talking to reporters on Wednesday. “What it does is extend the time in which you can rehire people, extend the time in which you pay back, and also undo the 75/25, which was debilitating,” referencing the requirement that 75% of loan proceeds be spent on payroll costs.

The House vote is expected next week. Still, with no Senate companion, the bill isn’t likely to move forward quickly. Negotiations between House and Senate leadership are on pause.