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Some delegations at the Republican convention signaled they would either vote against Mr. Lieberman’s nomination or walk out of the convention.

Meanwhile, Sen. Kay Bailey Hutchison, Texas Republican, told Fox News that she is not in the running and said she expects the pick to be Mr. Romney.

Playing defense Thursday morning, Obama campaign manager David Plouffe and chief strategist David Axelrod previewed their lines of attack for some of Mr. McCain’s choices.

“Whoever he picks doesn’t change the fact that it’s John McCain’s agenda on the ballot,” Mr. Plouffe said. “If you liked the last eight years … he’s going to give you more of the same Bush economic policies.”

If he chooses Mr. Romney, “all he’s done is sort of double down on out of touch, and being on the side of the big corporate special interests,” Mr. Plouffe said. “Romney’s an expert on things like Cayman Islands tax shelters.”

Mr. Axelrod suggested that Mr. McCain has sold out to conservatives in his party by appearing to back away from naming a pro-choice running mate.

“You’ve seen … basically people in his party holding a gun to his head and saying you cannot pick a pro-choice candidate and setting the parameters of this,” he said. “He’s not been fully embraced by conservatives in the party and now he’s not really trusted by moderates either because he’s made this Faustian bargain to be the nominee of the Republican Party.”

Mr. Pawlenty, in Denver to headline the Republicans’ response for the day, told reporters he planned to be at Minnesota’s state fair Friday, rather than campaigning with Mr. McCain in Ohio.

But his performance at the press conference made it clear he thought he was still in the running.

Despite the presence of other top Republicans, Mr. Pawlenty fielded most of the questions, aiming the kinds of barbs at Mr. Obama that a running mate is expected to fire.

He also did not shy away from listing the credentials that could make him an acceptable vice president: six years as governor, and before that state Senate majority leader. And he noted that being governor means being commander in chief of Minnesota’s National Guard.

Ralph Z. Hallow, reporting from Minneapolis, Christina Bellantoni in Denver, and Joseph Curl, traveling with the McCain campaign, contributed to this article.