As Mr. Romney and Mr. Santorum traded a new round of sharp charges in Michigan on Saturday, some Republican leaders expressed concern about the effects of a prolonged and nasty primary fight.

“The general election prospects for Republicans certainly would be better served if more focus was spent on Obama’s policies and the failures of those policies,” said Haley Barbour, the former governor of Mississippi and a longtime party leader. “There’s still time for that, but it would improve our prospects greatly.”

Mr. Barbour was speaking at the winter meeting of the National Governors Association in Washington, where the presidential race and the alarm over its intense negativity were central topics.

Gov. Rick Snyder of Michigan, who endorsed Mr. Romney, said he was disappointed by the acrimony that had overshadowed plans to create jobs and lift the economy. “That’s what citizens care about,” he said. “They don’t like all the bickering. It does not add value.”

Gov. Mitch Daniels of Indiana said it had fed his fears that “our side might not offer a bold enough and specific enough and constructive enough — and I would say inclusive enough — alternative.” He said the Republican race would almost certainly not be settled by May 8, the date of the primary in his state.

Indeed, Mr. Romney’s campaign has warned donors and supporters that even with his victories in the coming contests, the Republican competition may very well last until at least the middle of May. They said the situation did not indicate diminishing prospects for Mr. Romney but rather was the result of the party’s delegate-allocation rules and the additional time those require for any candidate to accumulate the 1,144 delegates necessary to secure the nomination.

The acknowledgment that the intraparty competition will most likely continue into the spring would seem to sweep aside the Romney campaign’s hope that it could string together a series of early victories sufficient to claim the nominee’s mantle — symbolically, at least — and begin focusing exclusively on Mr. Obama.