Davis supporters say their candidate would do well because his 11th District includes Northern Virginia’s Fairfax and Prince William counties.
Conservatives disagree with some of Mr. Davis‘ political views, but acknowledge he might be the best candidate in the general election.
Mr. Davis, 58, has been raising his profile among Republicans in the more conservative southern part of Virginia. He has had dinner with party leaders and plans another swing through the region next month.
Such efforts are necessary, considering that the party’s anti-tax conservatives in the primaries June 12 defeated two state Senate incumbents who sided with Democrats in 2004 to pass a $1.38 billion tax increase.
Observers say the results show the strength of Mr. Gilmore and other conservatives who promise to retain the tenets of less government and taxation.
“I think a strong conservative candidate would probably win our nomination,” Mr. Blackwell said.
The Republican winner faces a potential challenge from Mark R. Warner, a Democrat and popular former governor who has been mentioned as a possible vice presidential candidate.
“It would be like the [World Wrestling Federation] cage match at the end of the year,” he said.