Updated

More than half the delegates to next week's Republican National Convention were willing to suggest a new running mate for President Bush if Dick Cheney (search) leaves the ticket, an Associated Press survey found.

Most interviews occurred before Cheney's comments Tuesday about his opposition to President Bush's call for a constitutional amendment banning gay marriage, remarks that produce an outcry among social conservatives in his party.

Roughly 9 percent of delegates named Powell, who spurned Bush's vice presidential overtur, considered a potential 2008 presidential candidate.

National Security Adviser Condoleezza Rice (search) was third at more than 7 percent, followed by two influential GOP senators — John McCain (search) of Arizona and Majority Leader Bill Frist of Tennessee.

Just a handful of delegates, like William Wiess Jr. of Phoenix, were vocal about their preference for someone other than Cheney.

"For the party, the best thing — a win for Bush — would be McCain," said Wiess, 43. "I think he brings the party more toward the moderate flanks."

McCain was the choice of almost 5 percent of delegates.

The single biggest response — about 45 percent — to the question, "If Vice President Cheney were to step aside, who would be your first choice to be President Bush's running mate?" was "None." That covered those who refused to answer questions, gave no response or declined to answer because they thought Cheney wouldn't be booted from the ticket in the first place.

Delegate Ron Schmidt, 67, a Republican National Committee member from Rapid City, S.D., called Cheney "a very positive force in the party."

"There's no rational basis for him to step aside. Not a single argument," he added.

Bush himself has made clear he wants to keep the ticket intact, and campaign officials insist that replacing Cheney never has been actively considered.

Bush's advisers are keenly aware that Cheney has high negatives — from his Halliburton connections to his strong push for war with Iraq and his prolonged insistence of ties between al-Qaida and Iraq.

Despite Cheney's decades of political experience, there is also worry among some Republicans about unfavorable comparisons with John Edwards, 50, the youthful-looking Democratic vice presidential candidate who has served one term in the Senate.

Still, Cheney is loved by the GOP's conservative base — many of whom will be on the convention floor — despite his recent comments about gay marriages.

Cheney's daughter Mary is a lesbian, and in a campaign stop Tuesday, the vice president said that people should be free to have the relationships they want, and existing law may be enough to uphold traditional marriage.

The AP surveyed about three-quarters of the 2,500-plus GOP convention delegates. Those willing to speculate about a name to replace Cheney didn't necessarily think there was any chance Bush would shake up the ticket.

"Be still my beating heart. Condoleezza Rice. If she refused, Colin Powell. I don't think we'll even get there anyway," said delegate William Black, 62, of Danville, Ill. "I just think that (a Rice or Powell candidacy) would be a tremendous opportunity for the party, given Mr. Cheney's health."

Cheney, 63, has had four heart attacks since 1978, the most recent coming in November 2000. The vice president had a pacemaker placed in his chest the following year and his last annual heart checkup in May yielded no signs of irregularities.

Polls show that people are evenly split on whether they have a favorable or unfavorable impression of Cheney. In contrast, people hold a favorable view of Edwards.

But replacing Cheney "would create a firestorm among conservatives in the Republican Party. There's no redeeming value for Republicans," said Terry Madonna, a political scientist at Franklin & Marshall College in Lancaster, Pa.

Besides, Madonna adds, vice presidential candidates historically have little bearing on the outcome of presidential elections since the spotlight is squarely on the top of the ticket.