Many Americans who haven't firmly settled on a presidential candidate still have unanswered questions about whether Democrat John Kerry (search) would make an acceptable president, new polling suggests.

The National Annenberg Election Survey (search) found that potential swing voters in the battleground states have not yet decided how they feel about Kerry. A fourth see him favorably and a fourth see him unfavorably, while almost four in 10, 38 percent, remain neutral about him.

Public opinion about President Bush (search) was more settled among the persuadable group, with people about evenly split but only one in five having a neutral view of the president.

"Opinions have not been firmly formed about Kerry yet," said Kathleen Hall Jamieson, director of the Annenberg Public Policy Center (search) at the University of Pennsylvania. "There is a large open question on whether Kerry can pass the presidential threshold."

While public approval of Bush has been sagging, both overall and in his handling of Iraq (search) and the economy, Kerry, the presumptive Democratic nominee, still remains close in head-to-head matchups in several recent polls.

The Annenberg survey, which does not release head-to-head results, looked at those who are persuadable in the battleground states, about 11 percent of the overall population.

"Among the persuadable voters, Bush still trumps Kerry on strong leadership, despite the fact that on some other indicators these are not happy people," Jamieson said.

While she said the election campaign remains wide open, "Bush is carrying some very important cards in this election."

Because Kerry must pass the presidential threshold with potential voters, "in large part, this is an election about Kerry," she said.

"Kerry hasn't passed the threshold yet to be perceived as a president," Jamieson said. "If he passes it, George Bush is in serious trouble."

The Annenberg survey focused on 832 persuadable potential voters in swing states out of 8,314 adults polled nationally during May.

Compared to the overall public, that group was gloomier about the economy and were less enthusiastic about Bush's handling of the economy.

On Iraq, a majority of those considered persuadable was more inclined to want to bring U.S. troops home as soon as possible. The overall public was split on that question.

The poll drew its persuadable sample — those who are undecided or could change their minds — from 20 swing states: Arizona, Arkansas, Colorado, Delaware, Florida, Iowa, Louisiana, Maine, Michigan, Missouri, Minnesota, Nevada, New Hampshire, New Mexico, Ohio, Oregon, Pennsylvania, Washington, West Virginia and Wisconsin.