Senator Clinton’s hopes to win the Democratic presidential nomination now rest on an increasingly tricky bank shot after Senator Obama of Illinois won the Wisconsin primary and Hawaii caucuses last night, extending his winning streak to ten.

To remain a viable candidate, Mrs. Clinton needs commanding wins in Ohio and Texas in two weeks, as well as in Pennsylvania in April. She will have to carry those states convincingly while fighting a strong headwind created by Mr. Obama, who seems to be reducing or erasing the New York senator’s lead in opinion polls.

Mrs. Clinton’s campaign had hoped that blue-collar, lower-income voters would make her competitive with Mr. Obama in Wisconsin, a state with little of the African-American constituency that has been loyal to the Illinois senator. However, exit polls found little evidence of traction for the former first lady beyond her base of older women.

With 99% of precincts reporting, Mr. Obama had 645,554 votes, or 58%, to 452,590, or 41%, for Mrs. Clinton.

At a speech in Houston last night, Mr. Obama noted his win in Wisconsin and cautioned his supporters against overconfidence. “The change we seek is still months and miles away, and we need the good people of Texas to help us get there. We will need you to fight for every delegate it takes to win this nomination,” he said.

In the Republican primary in Wisconsin, the front-runner, Senator McCain of Arizona, was declared the winner by television networks last night as soon as polls closed. With 99% of precincts reporting, he had 224,122 votes, or 55%, compared to 151,114, or 37%, for his nearest rival, Michael Huckabee. Mr. McCain was also declared the winner of Washington state’s Republican primary. With 56% of precincts reporting, he had 183,702 votes, or 49%, to 80,351, or 21%, for Mr. Huckabee.

A total of 74 Democratic delegates and 37 Republican delegates were up for grabs in the Badger State. In Hawaii, 20 Democratic delegates were due to be allocated at caucuses last night. With 68% of precincts reporting Mr. Obama, who was born in Hawaii and spent much of his youth there, had 20,974 votes, or 76%, to 6,529, or 24%, for Mrs. Clinton.

Before last night’s results, Mr. Obama was leading Mrs. Clinton in the delegate count, 1,281 to 1,218. In the Republican delegate race, Mr. McCain led Mr. Huckabee, 908 to 245.

Mrs. Clinton’s hopes to change the dynamics of the race seem to rest now on two upcoming debates: one set for Austin, Texas, tomorrow and another in Cleveland on February 26.

Aides to the former first lady signaled yesterday that she will be toughening her rhetoric against Mr. Obama.

“Both Senator Obama and I would make history, but only one of us is ready on day one to be commander in chief, ready to manage our economy, and ready to defeat the Republicans,” Mrs. Clinton was to say in Ohio last night, according to excerpts of her remarks released in advance. “One of us has faced serious Republican opposition in the past. And one of us is ready to do it again.”

Mrs. Clinton’s campaign said she would offer more sharp contrasts with the Illinois senator in a “major address” she is to deliver this morning at a fund-raising event at Hunter College in Manhattan.

In Texas last night, Mr. Obama appeared to offer a rebuttal of sorts as he argued that inspiring people was necessary to form a “working majority for change.”

“It is going to take more than big rallies. It’s going to require more than rousing speeches. It will also require more than policy papers or positions and Web sites,” the Illinois senator said. “The problem that we face in America today is not a lack of good ideas. It’s that Washington has become a place where good ideas go to die. … The last thing we need is to have the same old folks, doing the same old things, making the same mistakes over and over and over again. We need something different.”

After the Wisconsin results came in, Mr. McCain made clear that he now considers his nomination to be inevitable. “Thank you, Wisconsin, for bringing us to the point where even a superstitious naval aviator can claim with confidence and humility that I will be our party’s nominee for president of the United States,” the Arizona senator told a rally in Columbus, Ohio. He did not call on Mr. Huckabee to drop out, but instead praised the former Arkansas governor for his “impressive grit and passion.”

In what could be a taste of the fall campaign, Mr. McCain took several swipes at Mr. Obama, suggesting that the Illinois senator is using hollow rhetoric to trick voters. “I will fight every moment of every day of this campaign to make sure that Americans are not deceived by an eloquent but empty call for change,” the Arizona Republican said.

Mr. Obama countered by saying he appreciated Mr. McCain’s military service, but that “he represents the policies of yesterday.”

According to exit polls conducted in Wisconsin by television networks and the Associated Press, women voting in the primary there favored Mrs. Clinton only slightly over Mr. Obama, 51% to 48%. Among men, the Illinois senator trounced Mrs. Clinton, 66% to 32%. Mrs. Clinton and Mr. Obama ran even among those with only a high school education, but the Illinois senator prevailed handily among those with any higher level of education.

In an interview yesterday before polls closed, Mr. Obama said for the first time that he may emerge as the party’s presumptive nominee soon after the voting next month in Ohio and Texas.

“I think it’s premature to talk about wrapping it up,” the Illinois senator told NBC. “We’ve got to campaign hard in Texas and Ohio, but after March 4 I think the party’s going to have to take a look and see if it’s time for us to go ahead and move forward with the nomination.”