House Budget Committee Chairman Paul RyanPaul RyanRyan reminds lawmakers to be on time for votes Lawmakers consider new security funding in wake of shooting Paul Ryan: ‘Beautiful day’ to catch up with Bono MORE (R-Wis.) on Sunday said he will not back down from the battle to repeal the 2010 Affordable Care Act even though some Republicans think the party should move on.

Ryan dismissed criticism that House Republicans have virtually no chance of dismantling the signature legislative accomplishment of Obama’s first term and their efforts might be better expended elsewhere.

He said his budget assumes the repeal of the healthcare law, in an interview on “Fox News Sunday.”

When host Chris Wallace challenged him on that assumption, Ryan said he would not give up the fight.

“That’s not going to happen,” said Wallace.

“We believe it should,” Ryan shot back. “That’s the point. This is what budgeting is all about. It’s about making tough choices to fix our country’s problems. We believe ‘ObamaCare’ is a program that will not work.

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“We believe ObamaCare will actually lead to hospitals and doctors and healthcare providers turning people away,” he said.

Speaker John BoehnerJohn BoehnerRyan reminds lawmakers to be on time for votes Juan Williams: GOP fumbles on healthcare The Hill's 12:30 Report MORE (R-Ohio) suggested shortly after Election Day that the political calculus had changed on repealing the controversial law, which fired up conservatives in the 2010 midterm election.

“Well, I think the election changes that,” BoehnerJohn BoehnerRyan reminds lawmakers to be on time for votes Juan Williams: GOP fumbles on healthcare The Hill's 12:30 Report MORE told ABC News’s Diane Sawyer when asked whether Republicans would still pursue repealing the law.

“It’s pretty clear that the president was reelected, Obamacare is the law of the land. I think there are parts of the healthcare law that are going to be very difficult to implement and very expensive,” he said.

Ryan, however, said he would accept the year-end fiscal deal that raised $620 billion in tax increases compared to 2012 policy but made most of the Bush-era tax rates permanent.

“We don’t want to refight the fiscal cliff. That’s current law. That’s not going to change,” he said.

Ryan said his budget would cut spending by about $5 trillion over the next 10 years.

He said his plan would slow spending growth to 3.4 percent per year, down from its current trajectory of 4.9 percent per year.

“Instead of spending $46 trillion over the next ten years, we’ll spend $41 trillion,” he said.