The Senate deadlocked Thursday over federal student loan interest rates, with no consensus in sight on how to prevent rates on certain loans from doubling for about 7 million borrowers on July 1.

Amid a swirl of competing proposals from lawmakers and the White House, preliminary votes showed that no Senate bills have the 60 votes needed to overcome a filibuster in the Democratic-led chamber.

Unless Congress intervenes, rates for new subsidized student loans will rise on July 1 from 3.4 percent to 6.8 percent. These loans, with the most favorable terms the government offers, are aimed at undergraduates who demonstrate financial need. They do not accrue interest while the students are in college.

On Thursday, the Senate blocked a Republican bill to peg rates on a variety of federal loans to the yield on the government’s 10-year Treasury bill, plus 3 percentage points. The vote was 40 to 57.

Then the Senate thwarted a Democratic bill to freeze for two years the 3.4 percent rate for subsidized loans. A procedural vote on the bill was 51 to 46, with Republicans solidly opposed.

“This is the opening act of the circus,” Sen. Lamar Alexander (R-Tenn.) said, urging lawmakers to find a bipartisan deal. “Won’t take too long. Will be a little embarrassing that we have to go through it.”

Sen. Tom Harkin (D-Iowa), chairman of the Committee on Health, Education, Labor and Pensions, contended that the Republican bill would hit students harder than passing no bill at all. “This is the worst possible approach,” Harkin said. “You shouldn’t reduce the deficit on the backs of students.”

In June 2012, faced with a similar rate-doubling threat, Congress froze the subsidized lending rate for a year. Other types of federal loans, with rates of 6.8 percent and 7.9 percent, are unaffected by the July 1 deadline.

Now there is talk of finding a longer-term solution that would overhaul rates for all federal loans. But the prospects for compromise are muddled beyond the usual partisan gridlock.

A chief reason is that President Obama’s position differs from the stance of many congressional Democrats. He wants a significant switch to market-based rates for all federal student loans; his usual Democratic allies on Capitol Hill want to freeze rates while continuing the debate.

In April, Obama proposed tying interest rates for subsidized and other federal loans to the government’s cost of borrowing, using the 10-year Treasury bill as a benchmark and adding a markup that would vary depending on the type of loan. Rates would vary from year to year but would be fixed for the life of an individual loan once a student borrows the money.

The Republican-led House approved a bill May 23 that would also set interest rates to the yield on the 10-year Treasury, plus a markup. That bill, unlike the Obama plan, includes an interest rate cap that proponents say would protect students.

Also unlike the president’s plan, rates for individual loans under the House bill would not be fixed but would rise or fall with the market each year. For that reason and others, the bill drew a veto threat from the Obama administration.

The Senate Republicans’ proposal, sponsored by Tom Coburn (R-Okla.), also relies on the 10-year Treasury as a benchmark, adding 3 percentage points. Rates would be about 4.8 percent this year. But the Coburn bill would fix interest rates for the life of an individual loan once the money is borrowed.

Asked Thursday afternoon whether the Obama plan could pass the Senate, Harkin said: “It needs some work. . . . There are some things the president proposed that we find troubling.”

Brandon Anderson, 28, a senior at Georgetown University, came to Capitol Hill with other students to lobby for a rate freeze. “A top university comes with a high price tag,” Anderson said. “I needed to take out federal student loans. . . . My message to Congress is, don’t double my rate.”