In Tight Virginia Senate Race, Seeking Every Edge PAUL, Va. - Like so many others in Appalachia, Amelia Trent's vote is tied to coal, and when it comes to the coal industry and her economic future, Ms. Trent does not trust President Obama. Obama is scary. He's a Muslim," Ms. Trent said matter-of-factly, but incorrectly, outside the small law firm here where she works as a secretary. On the other hand, she said she could never vote for Mitt Romney. He doesn't know what poor is - or the struggling middle class, which is what we are around here. But Ms. Trent, 59, knows and likes former Gov. Tim Kaine, the Democrat contending for the seat of Senator Jim Webb, a fellow Democrat who is retiring. She said she would vote for him over former Senator George Allen, a Republican trying to win his seat back in a neck-and-neck race that could decide which party controls the Senate. Of more than a dozen competitive Senate races this year, none appear as close as the contest in Virginia. For both Mr. Kaine and Mr. Allen, the search for people like Ms. Trent who say their vote for senator is not tied to their vote for president has become imperative. The state appears deadlocked between Mr. Obama and Mr. Romney. A Quinnipiac University poll released on Thursday had the presidential candidates even at 44 percent support in the state, a situation consistent with recent national polls. The poll also showed the Senate race tied. And neither Senate candidate wants his fate dependent on his party's presidential standard-bearer. In this hunt for voters, however, Mr. Kaine sees an edge, if only a small one. He was Mr. Obama's handpicked Democratic National Committee chairman, and he has made no real effort to distance himself from the president. Last weekend, he stood side by side with Mr. Obama as the president barnstormed Virginia. Still, Mr. Kaine portrays himself as a bipartisan problem solver in the mold of Virginia's other senator, Mark Warner, another Democrat who courted both parties while serving as governor. Mr. Kaine has tried to appeal to swing voters in the Washington suburbs, including moderate Republicans, with his record on transportation issues in the region. And his time as a moderate mayor of Richmond could still appeal to some Republicans there. His language is carefully chosen. At a roundtable discussion in Bristol, hard on the Tennessee border, Mr. Kaine told attendees from both parties: "I'll make this promise to you: If I'm elected, I will be a partner with the president, whoever it is." Mr. Allen, by contrast, has made Mr. Obama - and Mr. Kaine's close connection to him - Issue No. In recent advertisements, including one first shown last week, Mr. Allen has sought a bipartisan sheen, but his record has a harder edge than his opponent's, including his famous pledge at the 1994 state Republican convention to knock Virginia Democrats" "soft teeth down their whiny throats." Asked whether she could envision someone who would vote for Mr. Romney and also for Mr. Kaine, Nancy Steele, a Republican bed-and-breakfast manager who attended Mr. Kaine's Bristol meeting, paused and then said no. Asked if she could see an Obama-Allen voter, she laughed and said, "Never!" But Mr. Kaine said he thought he could appeal to those who vote for Mr. Romney. "There will be thousands of Romney-Kaine voters," Mr. Kaine said over a milkshake in Bristol. Whether it will be 2,000 or 50,000, I don't know. Kaine campaign aides say the mother lode of Romney-Kaine voters is not in the less populated country roads of southwestern Virginia but in the suburbs of Washington and Richmond. There, some voters may see Mr. Kaine and Mr. Romney as pro-business technocrats - and Mr. Allen and Mr. Obama as partisan flag carriers for their parties. But Mr. Kaine is searching for them across this diverse state. The trip to Bristol last week was his third. He has also been to the conservative southwestern towns of Castlewood, Wise and Blacksburg, and he is planning another trip this month, to a health clinic at the Wise County Fairgrounds. No one expects the Democrat to win this area, but he cannot afford to be blown out. "There's some tough real estate in this state," Mr. Kaine said, "and this is some tough real estate." The Allen campaign believes that Mr. Kaine is facing a rout in coal country, where many white working-class voters are suspicious of Mr. Obama's intentions for coal. To distance himself from the president, Mr. Kaine would have to offer vocal opposition of the sort that Senator Joe Manchin, Democrat of West Virginia, displayed in an advertisement that showed him firing a rifle at an Obama energy bill, said Chris LaCivita, a longtime Virginia Republican campaign adviser. But that will not happen.