McConnell, appearing with other Republican leaders after a Republican policy lunch, said Obama has not identified how the legislation would be funded. He called the dispute a "manufactured controversy" and said he sent the White House a letter last week listing four funding means with which Obama has said in the past he agreed.
"We're waiting to hear back from the administration which one of their recommended pay-fors they might want to adopt to resolve this impasse and prevent student loan rates from going up," McConnell said.
Education Secretary Arne Duncan told reporters at the daily White House briefing that "obviously all of us want to get this thing done and get it done before July 1," saying the president "has worked extraordinarily hard" on the issue.
"If the Republicans are getting serious about that, that's fantastic," he said. "And we hope, over the next couple weeks, we fully expect Congress to do the right thing and to solve this and solve it in a bipartisan way."
Asked if he was open to a compromise on offsetting the cost, Duncan replied, "I don't think it's my job to negotiate from here," but the administration's goal is to have it resolved by July 1.
"That's critically important," he said. "We can't afford to take this step in the wrong direction. We have to keep those Stafford interest rates low. And we're committed to doing that, and absolutely hope and expect the Republicans to work with us in a bipartisan way to get this done -- not to talk about it, but to fix it."
Republicans were harshly critical of Obama on every front.
"The president is fond of blaming others for the problems of the country," said Sen. Jon Kyl, R-Ariz., the minority whip.
Sen. John Barrasso, R-Wyo., chairman of the Senate Republican Policy Committee, said the administration's insurance mandates will make policies for college students either far more expensive or unavailable.
"Now, remember it was the president who said, 'If you like what you have, you can keep it,' but for hundreds of thousands of college students, that's not the case," Barrasso said.
Obama made the remark to which Barrasso alluded in reference to healthcare coverage, not student loans.
Duncan and Consumer Financial Protection Bureau Director Richard Cordray participated in a roundtable with Vice President Joe Biden and a number of presidents of colleges and universities to discuss ways to provide students with more transparency about college costs to help them make their financial decisions.