House GOP leaders are expected to discuss whether or not to extend a rate cut on student loans at a meeting Wednesday morning.
On Tuesday, top Senate leaders from each party indicated they had reached an agreement but were waiting to hear whether House Republicans would accept the deal.
The White House issued a statement praising the Senate deal and pressed House Republicans to accept it.
"We're pleased that the Senate has reached a deal to keep rates low and continue offering hardworking students a fair shot at an affordable education," White House Press Secretary Jay Carney said in a statement. "We hope Congress will complete the legislative process and send a bill to the president as soon as possible."
House GOP leaders were still looking at the details, said Michael Steel, a spokesman for House Speaker John Boehner. He also declined to say whether they would bring the deal up for a vote in the House.
For days, Senate leaders had stopped just short of announcing a deal out of fear their agreement might be rejected by GOP conservatives in the House, who have concerns about the way the nearly $6 billion price tag of the bill is offset. In particular, they don't like changes to two pension-related items that could raise the costs businesses pay for their employees' pensions.
Senate Democrats said Boehner's office has been in close contact with Senate Minority Leader Mitch McConnell's office throughout the negotiations and hopefully will be able to get GOP members to approve the deal.
"The president has been largely uninvolved" in the talks, McConnell said. "But (Senate Majority Leader Harry Reid) and I have an understanding that we think will be acceptable to the House."
McConnell wasn't the only Republican critical of President Obama's level of involvement in the talks.
"Did the White House read about an agreement on CNN.com?" asked a senior House GOP aide. "Because their level of involvement has been zero."
The Senate leaders also said they are considering pairing the student loan bill with a long-stalled transportation funding measure known as the highway bill, which is still being negotiated between the House and Senate. Doing so could save time as the two chambers race to beat the clock and leave town for the Fourth of July recess at the end of the week.
They also hope it will make it harder for conservatives to oppose the pension offsets because one of them is being used as a funding measure for both bills.