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Mr. Latimer said the Romney campaign’s decision to exclude Mr. Bush wouldn’t fool any voters, and that the move seemed to be driven by polls.

“He was the last Republican president and was elected to two terms. [Mr. Romney] thinks Americans forgot that? What would the Romney people do if Ann Romney didn’t poll well?” Mr. Latimer said.

But Sen. James M. Inhofe, Oklahoma Republican, said it was better not to have Mr. Bush at the convention, both because Democrats would use his presence as a way to try to tie Mr. Romney to the former president, and because it could change the convention’s goal of highlighting contrasts between Mr. Romney and Mr. Obama.

Still, Mr. Inhofe said there is reason to think that Mr. Bush’s reputation will continue to rise as voters compare his record with that of Mr. Obama over the past four years.

George Bush may have looked pretty bad a couple years ago, but he looks a lot better today,” said Mr. Inhofe, who is poised to become chairman of the Senate Environment and Public Works Committee should Republicans gain control of the Senate in November.

The Bush legacy isn’t completely absent from the convention. Ms. Rice will speak, as will Sen. Rob Portman, who served as Mr. Bush’s trade ambassador and budget director before winning his Senate seat in Ohio.

Mr. Bush’s younger brother Jeb, who was two-term Florida governor, also will address the delegates here.

Mr. McKenna said Jeb Bush earned his spot by being a “tremendously popular figure” among Florida Republicans and the broader conservative movement.

“If his last name was Jones instead of Bush, he would be accepting the nomination right now,” Mr. McKenna said. “I don’t think there’s a doubt in anybody’s mind that he could be a great, great president.”

As for the contrast between Democrats’ and Republicans’ treatment of their former presidents, Mr. Blakeman said having Mr. Carter speak at the Democratic convention was “a gift” to Republicans. He said it will highlight the tough economic circumstances both Mr. Carter and Mr. Obama faced — and will contrast them with the boom times of the Clinton years.

Clinton is going to remind the Democrats of what they like, and Carter’s going to remind them of what they’ve got. It’s a terrible contrast,” he said.