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.