House Speaker John Boehner (R-Ohio) said he got "98 percent" of what he wanted in the final deal to raise the debt ceiling.
"When you look at this final agreement that we came to with the White House, I got 98 percent of what I wanted. I'm pretty happy," Boehner said in an interview with CBS News on Monday evening.
He also said he expected to remain Speaker of the House.
Some political observers speculated Boehner's Speakership was on the line as he sought Republican support for a compromise agreement congressional leaders negotiated with the White House.
The measure passed the House Monday 269-161, with 174 Republicans backing the bill. Sixty-six Republicans voted against the plan.
The deal is expected to pass the Senate on Tuesday, just barely ahead of the deadline the Treasury Department set for when the U.S. government would default if a deal to raise debt limit were to have failed.
According to the Congressional Budget Office, the deal cuts federal deficits by $2.1 trillion over 10 years while also raising the debt limit by an equal amount. The deal also creates a joint, bicameral committee of legislators charged with finding additional cuts.
The compromise includes no added revenues; the House and Senate will vote on a balanced-budget amendment at some point in the last quarter of 2012. Both a bill without revenues and a balanced-budget amendment had been a sticking point for conservative Republicans throughout the negotiations.