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But fact checkers poked Mr. Ryan for suggestions that the Obama administration was responsible for a manufacturing plant closing in his hometown of Janesville, Wis.

Democrats blasted him for criticizing Mr. Obama for failing to heed the recommendations of the Bowles-Simpson deficit commission — even though Mr. Ryan himself was on the commission and voted against the final report.

Now the polling shows Mr. Obama has once again opened up a significant lead over the Romney-Ryan ticket.

Jim Manley, a Democratic strategist who spent years as a staffer on Capitol Hill, said selecting Mr. Ryan has brought more scrutiny to the two budgets he wrote for House Republicans, and also to social issues such as abortion, where Mr. Ryan’s pro-life record of opposing abortion in all cases except where the life of the mother is at stake has drawn scrutiny.

“He had a reputation — I don’t think well-deserved — within the Washington press corps as being a serious thinker,” Mr. Manley said. “Now that people have had a chance to get beyond the editorial page of the Wall Street Journal and look at specifics, they see his budget doesn’t add up.”

Mr. Ryan wrote two budgets that passed the House, but both stalled in the Senate. Senate Democrats defeated Mr. Ryan’s plan but never offered one of their own.

His plans included a call for a major overhaul of the tax code and of Medicaid and Medicare. On that latter program, he proposed a voucherlike system that would apply to seniors 10 years from now, and would give them a choice of traditional Medicare or a private plan paid for by the government.

Rep. Michael K. Simpson, an Idaho Republican who serves on the Budget Committee with Mr. Ryan, said picking him means congressional Republicans will face even more questions about that Medicare plan, but he said that was inevitable. He said Mr. Ryan gives the GOP a good spokesman on the issue.

“It’s a debate that’s going to happen. The question is whether the American people are ready to have that debate or not,” he said.

Mr. Simpson said picking Mr. Ryan has been good for Mr. Romney and the ticket — though he was uncertain whether it had been good for the prospects for Mr. Ryan himself.

Indeed, Mr. Ryan has gone from a man of big ideas and bold votes — including regularly voting last decade against the GOP’s own spending bills — to a cautious vice presidential candidate who has to run his words and stances by the Romney campaign.

In the latest example, the House will vote later this week on a stopgap spending bill to keep the government running into 2013. Funding would otherwise run out Sept. 30, resulting in a government shutdown.

On Monday, Mr. McCarthy told reporters Mr. Ryan would be back at the Capitol for the vote and said Mr. Ryan will support the legislation — then stepped back from those comments and said the vice presidential nominee should answer for himself.

After first saying they didn’t have an answer, Mr. Ryan’s staffers late Tuesday said he will vote for the spending bill.

That vote does have some peril.

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