Over the long term, the GOP plan would transform the nation's Medicare program, changing it from a government-run system that pays seniors' health bills into a system where seniors buy insurance plans subsidized by the federal government.
Boehner said Ryan's budget proposal is "a serious step in the right direction."
"I'm just hopeful that the president will begin to get serious about the long-term fiscal crisis that our country is facing. It's serious," Boehner said. "It needs to be dealt with now, and we owe it to the American people, we owe it to our kids and grandkids to begin to cut spending and begin to transform these programs so that we can save Medicare, Medicaid and Social Security."
Democrats have decried Ryan's budget resolution as a proposal that would "change Medicare as we know it."
"It is an ethic for our country to keep our bedrock promise to our seniors, to keep our promise of Medicare, a benefit they have earned through a lifetime of work. House Republicans are voting to break that promise, jeopardizing the health and economic security of America's seniors," said House Minority Leader Nancy Pelosi, D-Calif.
"Seniors know that the Republican budget means -- all of you here who want hands off your Medicare know 'hands off' means end -- what they're trying to: end Medicare and shift health costs to seniors. No," she said.
"We've always said we will judge every initiative that comes before us as to whether it creates jobs, as it reduces the deficit, strengthens the middle class and continues the economic growth of our economy," Pelosi said. "This budget does none of the above, as it ends Medicare. Hands off our Medicare."
At a campaign fundraiser in Chicago this week, Obama used some harsh rhetoric on Ryan, whom he has publicly praised in the past for offering serious attempts to address the deficit.
"Eliminating the health care bill would cost us $1 trillion," Obama said. "It would add $1 trillion to the deficit. So when Paul Ryan says his priority is to make sure, he's just being America's accountant and trying to, you know, be responsible, this is the same guy that voted for two wars that were unpaid for, voted for the Bush tax cuts that were unpaid for, voted for the prescription drug bill that cost as much as my health care bill -- but wasn't paid for. So it's not on the level. And we've got to keep on keep on shining a light on that."
The House now adjourns for a two-week recess, and many members say they're anticipating a vibrant debate on the looming debt crisis in their districts.
"It's important for our members to go home and talk about the crisis that we face, and the fact that the changes being proposed would not affect one senior citizen in America -- not one -- because Paul's made it perfectly clear that anyone who's 55 years and older will not be affected by any of these changes. But if you're 54 and younger, those Americans understand if we don't make changes, the programs won't be there," Boehner said.
"I think it's pretty clear that if we don't make changes to these big programs, that they won't exist," he said. "And the fact is, is that the responsible plan put forward in the Path to Prosperity will, in fact, reform these programs and make sure that they're around for the long term. And understand: The greatest danger that America faces today is doing nothing."