Mr. Romney is within striking distance of Mr. Obama in Wisconsin, according to several public and private polls and interviews with strategists in both parties, and he intends to start building a campaign operation off the robust get-out-the-vote machinery assembled for Mr. Walker. The decision by the Romney campaign to try to contest Wisconsin is the first sign that Republicans are eager to expand their targets of opportunity and compete on terrain that not long ago seemed squarely on Mr. Obama’s side.

“If we win on Tuesday, this is going to be a shot in the arm and adrenaline that we didn’t expect to have,” said former Gov. Tommy G. Thompson, a Republican who is seeking the party’s nomination to run for Senate. “It is going to spark fervor in the presidential race.”…

Representative Paul D. Ryan of Wisconsin said Republicans were no longer in a “defensive crouch” after losing the state so soundly in the last presidential race. But the state is known for its share of ticket-splitters, he said, and he has bumped into some people supporting Mr. Walker who may still back Mr. Obama.

“There’s a slice of those Obama-Walker voters who think the recall is wrong, improper, a waste of money and an overreaction,” Mr. Ryan said. “But I see an awakening of citizens participating. It will show that our state is really in play in November.”