Rep. Paul Ryan (R-Wis.) said Sunday that the budget blueprint he plans to unveil this week will promote repealing President Obama’s signature health-care law.

“Yes, our budget does promote repealing Obamacare and replacing it with a better system,” Ryan, chairman of the House Budget Committee, said on “Fox News Sunday.”

Past House Republican efforts to repeal the president’s health-care law failed, and the Supreme Court upheld the constitutionality of the law last year.

Ryan’s budget proposal, which includes controversial proposals for giving states more authority over Medicaid, is sure to encounter stiff resistance from Democrats in Congress who are committed to protecting Obamacare. That push back is likely to complicate Obama’s efforts this week to advance a dialogue he reopened with Republicans last week on reaching a grand bargain on budget cuts and entitlement reform.

On Thursday, Ryan lunched at the White House with Obama and Rep. Chris Van Hollen (Md.), the ranking Democrat on the House Budget Committee. Ryan said Sunday that only time will tell how effective the president’s recent outreach to him and other congressional Republicans will be.

“The proof will be in the coming weeks as to whether or not it is a real sincere outreach to find common ground,” Ryan said.

The 2012 Republican vice-presidential candidate made his comments as he pitched a budget proposal that would wipe out the deficit in 10 years rather than in more than 20, as he proposed last year.

He said the more ambitious timetable would “not really” require much deeper cuts than those outlined previously, because of recent events. They include a rise in tax rates for the very wealthy enacted in January, and budget sequestration that took effect this month.

“We don’t have to do huge things to get the balance because of the new baseline,” he told “Fox News Sunday” host Chris Wallace.

Key parts of Ryan’s plan are items he and Mitt Romney campaigned on in the election they lost to Obama in November.

One is turning Medicare from a one-size-fits-all insurance program to one that helps subsidize the purchase of policies “based on who you are — total subsidy for the poor and the sick, less of a subsidy for wealthy seniors.” Another is turning Medicaid, which pays for health care for the very poor, into a block-grant program that would allow states to craft their own programs.

Ryan’s budget calculus includes a $770 billion cut to Medicaid over the next 10 years. Under Obama’s health-care plan, Medicaid would expand rather than contract, bringing in about 20 million more users.

Asked whether his plan was realistic, Ryan averred that parts of it were not.

“Will the president take our premium support program and block-granting Medicaid? My guess is he won’t,” Ryan told Wallace. “We think that’s the best way to make these programs work better. But are there things you can do short of that — that gets you closer to balancing the budget, that delays the debt crisis from hitting this country? Yes, I think there are.”

Ryan said the lunch at the White House was “the first time I’ve ever had a conversation with the president lasting more than, say, two minutes, or televised exchanges. I’ve never really had a conversation with him on these issues before.”

Sounding a conciliatory note, Ryan said: “I think there are things that we can do that don’t offend either party’s philosophy, that doesn’t require someone to surrender their principles.”

Republicans on other Sunday talk shows also expressed hope that Obama’s gestures would lead to substantive negotiations.

“I think he’s genuinely reaching out,” Sen. Tom Coburn ­(R-Okla.) said on NBC News’s “Meet The Press.” “But you know, you’ve got a lot of scabs and sores on people, and it’s going to take awhile for that to heal.”

Sen. Ronald H. Johnson (R-Wis.), one of Obama’s dinner guests, said on ABC News’s “This Week With George Stephanopoulos” that he would “give the president the benefit of the doubt.”

Both Coburn and Johnson were among a group of Republican senators who dined with Obama last week. The president is set to meet with leaders of both parties on Capitol Hill this week as the budget debate heats up.

Discuss this topic and other political issues in the politics discussion forums.