Sen. John Edwards (search), the smooth-talking populist who emerged from the nominating campaign as John Kerry's (search) chief rival, is favored among registered voters to be the Democratic vice presidential candidate, according to an Associated Press poll. But his name on the ticket does not automatically boost Democratic prospects.

A Kerry-Edwards pairing ties with the GOP tandem of President Bush and Vice President Dick Cheney (search), which is no better than Kerry's current showing in head-to-head matchups against Bush, according to the AP poll conducted by Ipsos-Public Affairs.

Kerry has made overtures to at least one potential candidate, Republican Sen. John McCain (search) of Arizona, who rejected the offer to forge a bipartisan alliance against Bush, The Associated Press reported Friday. Two officials familiar with the conversations said Kerry stopped short of formally offering McCain the job, sparing the Massachusetts senator an outright rejection that would make his eventual running mate look like a second choice.

Democratic strategists cautioned against reading too much into any poll before Kerry selects a running mate.

"Polling information on potential running mates is soft and unreliable because it's all about name identification and hypothetical," said Doug Sosnik, a top adviser in the Clinton White House. "Eventually, we'll have a campaign when people will get to know them. Right now, it's just mush."

The AP poll showed that more than one-third of registered voters — 36 percent — said they would most like to see Kerry choose Edwards.

Among Democrats surveyed, Edwards fared even better: 43 percent preferred him over three other Democrats.

The first-term senator from North Carolina remained in the primaries longer than any other major candidate and won over thousands of Democratic voters with the positive tone of his campaign.

The poll showed that 19 percent of registered voters wanted Rep. Dick Gephardt (search) of Missouri, the longtime Democratic leader who is retiring from the House. Eighteen percent chose retired Army Gen. Wesley Clark (search), a political newcomer from Arkansas, and 4 percent picked Gov. Tom Vilsack (search) of Iowa, a relative unknown on the national scene.

About 23 percent said they were not sure or they offered another name.

When Sen. Hillary Rodham Clinton (search) of New York was added to the mix, one-fourth of the respondents supported her while Edwards' backing remained strong at 34 percent. She picked up one-half of the black vote, drawing support from Gephardt, Vilsack and the "not sure" category.

She repeatedly has ruled out accepting the vice presidential nomination, and Kerry has not offered it.

Among just Democrats, Gephardt got 19 percent, Clark 18 percent and Vilsack 4 percent.

None of the potential candidates made much of a difference in a hypothetical matchup against the White House team.

Like the Kerry-Edwards tandem, a Kerry-Gephardt ticket tied Bush-Cheney while pairing Kerry with Vilsack or Clark resulted in a slight lead for Bush-Cheney.

"What this poll shows is that since Edwards ran a very, very competitive Democratic primary and stayed in until the bitter end and by all accounts acquitted himself well, he is favored by Democratic and all American voters," said Doug Schoen, a pollster for Clinton.

Schoen and other political experts say there is no way to measure the boost or drag a running mate will bring to the ticket.

Nobody predicted that Sen. Joe Lieberman (search) of Connecticut would give Democrat Al Gore the lift he did in 2000 nor did anyone foresee the problems Republican Dan Quayle (search) caused then-Vice President George H.W. Bush in 1988.

Whatever the impact, it is usually short-lived.

"Polling should be a factor on the final selection of a vice president, but I wouldn't put it on the top four or five factors," Sosnik said.

Presidential nominees are usually more interested in whether candidates are qualified to serve as president, whether there are any political problems in their background and whether the relationship would have some chemistry and trust, Sosnik said.

Schoen said Edwards benefits from being the last major candidate standing against Kerry in the Democratic race. Gephardt bowed out after a dismal fourth-place showing in Iowa's kickoff caucuses. Clark lasted longer but criticized Kerry along the way. Edwards jabbed at the Democratic front-runner but never made personal.

The AP-Ipsos poll of 788 registered voters was conducted Monday to Wednesday. The margin of sampling error was plus or minus 3.5 percentage points. For the responses of subgroups, it was slightly larger: 5 percentage points for Democrats, 5.5 percentage points for Republicans.

In hypothetical matchups against the GOP ticket:

— Kerry-Edwards had 47 percent to 44 percent for Bush-Cheney.

— Bush-Cheney had 47 percent to 45 percent for Kerry-Gephardt.

— Bush-Cheney had 47 percent to 43 percent for Kerry-Vilsack and for Kerry-Clark.

Kerry is expected to announce his choice next month.

Among others mentioned as potential Kerry running mates are Sens. Bob Graham of Florida and Evan Bayh of Indiana; former Sen. Bob Kerrey of Nebraska; and Govs. Janet Napolitano of Arizona, Mark Warner of Virginia, Bill Richardson of New Mexico and Ed Rendell of Pennsylvania.

Democrats say there may be a dark horse under consideration, perhaps a Republican other than McCain. Sen. Chuck Hagel, R-Neb., has been mentioned as a potential pick.

As for the Republican ticket, 28 percent of GOP voters surveyed thought Bush should pick someone other than Vice President Dick Cheney as his running mate.