Republican Craig Thomas, who says he's the rightful heir to former Rep. Dick Cheney, has built momentum in the final days of his race against Democrat John Vinich for Wyoming's lone House seat.

Officials of both campaigns say their polls show Thomas has pulled even or slightly ahead of Vinich. Voters on Wednesday will select a successor to Cheney, who resigned to become defense secretary.The two are vying to represent the nation's least populous state, but the contest's importance is far greater than the number of voters suggests.

The GOP is seeking to rebound from defeats in two special House races in Indiana and Alabama during the past month. Most embarrassing was the loss of Vice President Dan Quayle's old House seat in Indiana to Democrat Jill Long last month.

Republicans have put money and manpower behind Thomas, including visits by Sens. Bob Dole of Kansas and Alan Simpson of Wyoming. But Vinich has been quick to criticize the GOP effort, suggesting that Thomas wasn't running his own campaign.

Thomas, a 55-year-old state representative who lost two races for state treasurer, has criticized Vinich as a liberal dependent on support from organized labor. The AFL-CIO is backing the Democrat.

The election will demonstrate "whether or not we want to continue to have the kind of moderate conservative representation that we had with Dick Cheney and we have with our senators, or whether we want to take a rather marked change of philosophy," Thomas said.

Vinich, 38, is bidding to become the state's first Democrat to sit in Congress since Cheney replaced Teno Roncalio in 1978. Vinich entered the race with better name recognition. The state senator fell just 1,322 votes short of upsetting Republican Sen. Malcolm Wallop last fall.

Vinich said he would be more able to instruct the Democratic majority in the House on Wyoming concerns. He claimed he has been promised a seat on the House Agriculture Committee if he wins.

Thomas said he had been guaranteed a seat on the Interior Committee.