Lawmakers acknowledge that the rate on a low-interest federal loan for millions of college students in financial need is likely to double on Monday because of a congressional stalemate over how to stop that from happening.

But Democratic senators said Thursday that the rate hike on new subsidized Stafford loans — to 6.8 percent from the current 3.4 percent — will be temporary and reversible.

Sen. Debbie Stabenow (D-Mich.) said the Democratic-led Senate is expected to vote July 10 on whether to take up a bill that would fix the rate for such loans at 3.4 percent for a year, retroactive to Monday’s increase.

“We’re going to keep at it until we get this done,” Stabenow said, adding that “the White House is completely in support of what we are doing.”

Whether the bill that Stabenow and 38 other Democrats are sponsoring will succeed is unclear. For weeks, the Senate has been in a logjam on student loans ahead of the rate-doubling deadline that was set a year ago.

On June 6, a motion to proceed to a similar Democratic bill, which proposed a two-year extension of the 3.4 percent rate, drew 51 votes of support, well short of the 60 required to overcome a Republican filibuster. That day, a motion to proceed to a Republican bill establishing market-based rates on various types of student and parent loans died on a vote of 40 to 57.

On May 23, the Republican-led House approved a bill largely on party lines that would tie interest rates to the government’s cost of borrowing. The House bill was forecast to produce an interest rate of less than 5 percent on Stafford loans for the coming academic year. The rate on individual Stafford loans under the House bill would vary from year to year with the rise and fall of the yield of the 10-year Treasury note but would be capped at 8.5 percent.

The Obama administration threatened to veto the House bill, saying that its variable-rate system would produce too much uncertainty for students and parents.

Rep. John Kline (R-Minn.), chairman of the House Education and the Workforce Committee, said in the weekly Republican radio address Saturday that the House has done its part to solve the problem.

“We’re in this predicament because politicians put themselves in charge of setting interest rates, guaranteeing exactly this type of down-to-the-wire uncertainty for students and their families,” Kline said. “What we need is a long-term solution that gets Washington out of the business of setting rates altogether.”

Kline said in an interview that he is optimistic about prospects for a deal, citing a bipartisan plan for market-based rates that emerged this week with support from Sens. Joe Manchin III (D-W.Va.), Lamar Alexander (R-Tenn.) and others. “There’s a lot of room here for a possible agreement,” Kline said.

President Obama also has offered a market-based approach. Under his budget, made public in April, all federal education loans would be pegged each year to the yield on the 10-year Treasury note. Unlike the House bill, the Obama plan would lock the interest rate once a student or parent takes out a loan. But the Obama plan drew criticism from some student advocates because it had no rate cap.

Last year, when Congress faced a similar issue, it froze the subsidized Stafford rate for a year at the urging of Obama and Republican presidential nominee Mitt Romney. But student-loan policy has drawn less attention this year now that the presidential election is over.