WASHINGTON — Senator Obama talked of introducing some Chicago toughness to his politics of hope today, seeking a rebound after Senator Clinton grasped victory in the New Hampshire primary. In the wide-open Republican contest, Senator McCain pressed to build on his New Hampshire win and named experience, knowledge and judgment as his calling cards in the races ahead.

Mrs. Clinton pored over election strategy in the first blush of her surprising success and indicated she’d compete in every big Democratic contest coming up this month rather than try to cherry pick her way to the nomination.

“I’m going to keep going as we take on all the rest of the contests between now and February 5th,” she said, back home in New York to “get grounded and take a deep breath” after a victory that surprised her own campaign, confounded the pollsters and shocked nearly everyone else. Two dozen states vote February 5.

Mr. Obama responded not just to his Democratic rival’s New Hampshire primary win but to attacks on him by her husband, former President Clinton

“I think that Senator Clinton, obviously, is a formidable and tough candidate, and we have to make sure that we take it to them just like they take it to us,” the Illinois senator said. “I come from Chicago politics. We’re accustomed to rough and tumble.”

Mr. Obama is bidding for resurgence in South Carolina and Nevada, which vote this month. Today, he received the endorsement of the 60,000-member Culinary Workers Union local in Nevada in addition to the backing of the state’s chapter of the Service Employees International Union.

Mr. Clinton complained in New Hampshire that Mr. Obama was getting a free pass from the scrutiny turned on Mrs. Clinton and likened the Illinois senator’s campaign to a “fairy tale.” Mr. Obama shot back today that “the real fairy tale is, I think, Bill Clinton suggesting somehow that we’ve been just taking a cakewalk here.”

Mr. McCain campaigned in Michigan, hoping to reprise his win there in 2000 just as he did in New Hampshire, staggering one-time poll leader Mitt Romney.

“I can throw a dart at a map of the world and show you a place where there’s national security challenges,” Mr. McCain said before a Grand Rapids rally. “I’m the only one that’s been involved in these issues for the last 20 years.”

Speaking to several hundred boisterous supporters at the Grand Rapids airport, Mr. McCain noted the state’s job losses and pronounced federal programs to help displaced workers a failure. “None of them work,” he said. “I will develop programs that work.”

In Boston, Mr. Romney sought to assure his top financial backers that he can win in Michigan and beyond, after disappointing second-place finishes in Iowa and New Hampshire. Mr. Romney was born in Michigan and his father was governor.

“It’s just getting started,” he told hundreds of supporters gathered at a convention center for a follow-up to his campaign’s “National Call Day” that raised an unprecedented $6.5 million a year ago. The former Massachusetts governor misstated results when he told them he’s received “more delegates than anybody else.” An AP analysis of primary results shows he is second in the delegate count, with 19. Michael Huckabee has 31.

Mr. Huckabee, winner of the Iowa GOP caucus and third-place finisher in New Hampshire, also is in contention for the January 15 Michigan contest. He flew to South Carolina today, eager to capitalize on a polling lead he enjoys there and woo the state’s religious conservatives, a bigger bloc of voters than he encountered in New Hampshire.

A former Tennessee senator, Fred Thompson, set South Carolina as his firewall for a campaign that has yet to take off. “I’m proud to say I am drawing a line in the sand in South Carolina,” Mr. Thompson said today in Sumter. He bypassed New Hampshire’s GOP campaign and finished last there.

He said he won’t change his style for political expediency. “What you see is what you get,” he said. “If they like that, I’ll be in great shape.”

New Hampshire placed Mrs. Clinton squarely back in the contest for the Democratic nomination after her third-place finish in Iowa and revived Mr. McCain’s hopes seven months after his campaign had seemed to be down for the count.

In 2000, Mr. McCain was knocked out of the race after a brutal South Carolina campaign during which he was the subject of a whisper campaign and so-called push polling. Voters were called and asked about Mr. McCain’s daughter, insinuating she was illegitimate. She was adopted from a Bangladeshi orphanage.

Now, his South Carolina supporters have set up a “truth squad” to counter any negative campaigning against him.

“Our goal is to set the record straight,” the state’s attorney general, Henry McMaster, a campaign co-chairman, said. “As soon as one of these negative attack ads goes up on the air or hits the mailboxes, we’ll let the voters know the truth.”

The victories for Mr. McCain and Mrs. Clinton were evidence of New Hampshire’s prickly habit of rejecting those chosen by Iowa voters a few days earlier and raised the prospect of a drawn-out nomination battle between two history-making candidates: Mrs. Clinton, who would be the first woman to hold the presidency, and Mr. Obama, who would be the first president of African-American descent.

Third place on the Democratic side went to a former senator, John Edwards, who said he would not drop out. Instead, he hoped to keep the race a three-way contest. “Two races down, 48 states left to go,” he declared.

Mayor Giuliani bolted New Hampshire even before the ballots were counted and headed to Florida, the state he expected to propel him in the polls.

With 99% of the New Hampshire vote tabulated before counters shut down for the night, Clinton had 39%, Obama 36%, and Edwards 17%. Governor Richardson of New Mexico trailed with 5%.

On the Republican side, McCain had 37%, Romney 31%, Huckabee 11%, Giuliani 9%, and Rep. Ron Paul 8%. Thompson got 1%.