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On Sunday, they campaigned together in front of overflow crowds in North Carolina before heading to Wisconsin for a quick stop.

One key question will be how they meld Mr. Ryan’s public positions with those of Mr. Romney, who has laid out some ideas that are not as detailed as the Budget Committee chairman’s.

In an interview on CBS’ “60 Minutes” program, they said they have talked about how to preserve Medicare for current retirees while working to offer more options going forward — a way to begin to adapt Mr. Ryan’s plans into the campaign framework.

Campaign advisers told reporters that Mr. Romney would be the top of the ticket.

Speaking at a campaign fundraiser in Chicago, Mr. Obama called Mr. Ryan “the ideological leader of Republicans in Congress.”

“He is a decent man, he is a family man, he is an articulate spokesman for Gov. Romney’s vision, but it is a vision that I fundamentally disagree with,” Mr. Obama said.

Rep. Debbie Wasserman Schultz, the Democratic National Committee chairwoman, said the Ryan budget plan “would really jeopardize seniors in nursing homes, potentially take 10 million students off of Pell Grants, cut health care, cut education.”

Paul Ryan and Mitt Romney would allow seniors to fall right through that floor because they would pull the rug out from under seniors, give them a voucher, tell them they are essentially on their own, drive up their health care costs and then cost their families even more,” Mrs. Schultz said on “Fox News Sunday.”

Republicans countered by arguing that the Ryan selection highlights the Obama administration’s lack of progress on issues such as the budget, the federal deficit and entitlement reform.

While Mr. Ryan’s 2012 budget proposal won House approval before being defeated in the Senate, Republicans noted that Senate Democrats have not been able to pass a budget in more than three years, and Mr. Obama’s own budget this year was defeated unanimously in both the House and Senate.

“There has been no effort whatsoever on the part of this administration to address the looming crises of Social Security and Medicare,” Sen. John McCain, Arizona Republican, said on “Fox News Sunday.” “Paul Ryan has taken the courageous steps to bring this issue to the forefront.”