After a hard-fought race in Wisconsin on Tuesday night, John Kerry (search) was happy to have escaped with a victory, while John Edwards' (search) near win gave him reason to continue the race, which he hoped had finally been narrowed to a two-man field.

"Today the voters of Wisconsin sent a clear message," Edwards told energized supporters at the American Serb Memorial Hall in Milwaukee. "The message was this: Objects in your mirror may be closer than they appear."

We've had "an enormous surge in the last few days. This is an amazing response," an upbeat Edwards told Fox News. "I'm out here fighting my heart out for every vote. I'm in this fight to win, and I'm going to go after it every way I know how."

In the days before the race, Kerry had led by a two-to-one margin, but he told backers in Middletown that he was happy with another win.

"The motto of the state of Wisconsin is 'Forward,' and I want to thank the state of Wisconsin for moving this cause and this campaign forward."

"Wherever we go, we're feeling the power of change that is sweeping across this nation," Kerry said, without acknowledging the narrow margin of victory.

In a battle for national media attention, Kerry began his remarks just after Edwards started his, forcing television stations to cut away from Edwards to show the winner.

"That was, just knowing this campaign, a shot across the bow, him saying 'Welcome to the big leagues,'" said Ceci Connolly, a Washington Post reporter and Fox News analyst.

Earlier in the day, Kerry said he -- not Edwards -- was running the kind of campaign needed to win the nomination.

"You can't run for president by cherry-picking states here or there. You have to run nationally. I think I've been the only one in recent weeks who's been doing that and proving the ability to win in those places nationally."

While Kerry campaigned for Nevada's caucuses on Saturday, Edwards and Howard Dean (search) were camped in Wisconsin.

"We play everywhere, unlike John Edwards and Howard Dean and anyone else is in the race," said Steve Elmendorf, Kerry's deputy campaign manager. "Winning is better than losing. We've won more states than anyone else."

Edwards rejected the Kerry camp's derision of his strategy, saying, "I've been competing everywhere."

Edwards, looked forward to a head-to-head match-up against the front-running Kerry, challenging him, "I would very much like to see a one-on-one debate with Senator Kerry."

Dean, whose campaign has been jolted by defections and turmoil, suffered another disappointing result in Wisconsin. He is planning a speech back home in Vermont on Thursday. Aides gave conflicting reports about whether this address would be his withdrawal from the race.

"You all made me so happy I could just scream," a subdued Dean told supporters in Madison, making light of his post-Iowa "I Have a Scream" speech (search). Speaking as if his campaign had already ended, he thanked unions for "sticking with us right through the end."

Dean accepted credit for himself and his supporters for charting a new course for this election season. "You have already changed the Democratic Party and we will not stop," he declared to cheering supporters. "You have already written the platform of the Democratic Party for this election."

"We are not done," Dean said, as he promised that his effort to change politics was not over, even though it appeared his campaign might be.

Dean may also announce the launch of an organization that would take advantage of his grassroots network to help Democratic candidates.

Fox News' Carl Cameron and Steve Brown and the Associated Press contributed to this report.