(CNN) -- Sen. Hillary Clinton got her campaign back on track with projected wins in the Texas, Ohio and Rhode Island primaries.

Sen. Hillary Clinton claimed victory in Texas, Ohio and Rhode Island. more photos »

Delegate-rich Texas and Ohio were considered must-wins for her campaign.

Clinton's Democratic rival Sen. Barack Obama, who claimed victory in Vermont, had won 12 straight contests since Super Tuesday on February 5.

Texas also held Democratic caucuses Tuesday, but it was too close to declare a winner.

"For everyone here in Ohio and across America who's been ever been counted out but refused to be knocked out, for everyone who has stumbled but stood right back up, and for everyone who works hard and never gives up -- this one is for you," Clinton said before supporters in Columbus.

"You know what they say," she said. "As Ohio goes, so goes the nation. Well, this nation's coming back and so is this campaign."

Obama congratulated Clinton on her victories but downplayed his losses. CNN's political team weighs in on the results »

"We know this: No matter what happens tonight, we have nearly the same delegate lead as we had this morning, and we are on our way to winning this nomination," Obama told supporters in Texas.

Sen. John McCain swept all four Republican contests on Tuesday to become his party's presumptive nominee. Read about McCain's victory

McCain won primaries in Texas, Ohio, Vermont and Rhode Island, giving him more than the 1,191 delegates needed to clinch the GOP nomination.

"I am very, very grateful and pleased to note that tonight, my friends, we have won enough delegates to claim with confidence, humility and a great sense of responsibility, that I will be the Republican nominee for president of the United States," McCain told supporters Tuesday night. Watch McCain claim victory »

Mike Huckabee dropped out of the Republican race after the results came in.

"It's now important that we turn our attention not to what could have been or what we wanted to have been, but now what must be -- and that is a united party," Huckabee told a crowd in Dallas. Watch Huckabee bow out »

McCain is slated to go to the White House on Wednesday to receive the endorsement of President Bush, according to two Republican sources.

The Arizona senator's campaign -- his second run for the White House -- was largely written off for dead last summer amid outspoken opposition from the party's conservative base, a major staff shakeup and disappointing fundraising.

But McCain said earlier Tuesday that he was confident he would emerge as the presumptive nominee by the end of the night.

McCain overwhelmingly won moderates and conservatives in Ohio, but he lost the evangelical vote to Huckabee, according to exit polls.

Obama's campaign pressed to extend voting by one hour in two Ohio counties. See county-by-county results in Ohio

"Due to reports of ballot shortages in Cuyahoga and Franklin counties, we requested a voting extension in those counties," said Obama spokesman Bill Burton.

A judge ruled to keep parts of Cuyahoga county open an extra hour.

In Texas, Clinton held a two-to-one advantage over Obama with Hispanic voters, while Obama had the overwhelming advantage with black voters in the state's Democratic primary, according to CNN's exit poll. See county-by-county results in Texas

Eighty-three percent of blacks voted for Obama, while 16 percent supported Clinton, according to the exit poll.

Meanwhile, 64 percent of Hispanics backed Clinton, while 32 percent went for Obama.

Early exit polls indicate a distinct "age gap" in both states.

Obama appealed most strongly to younger voters while older voters favored Clinton. Among Ohio Democratic primary voters aged 17 to 29, 65 percent went for Obama, and 34 percent went for Clinton. Among those age 60 and older, Clinton led Obama 67-31 percent.

The same pattern held true in early exit polling from the Texas Democratic primary. Among voters aged 18 to 29, Obama led Clinton 61-39 percent, and among voters 60 and older, Clinton led Obama 63- 36 percent.

Poll workers in Collin County, near Dallas, estimated that nearly three-quarters of the Democratic voters would participate in the Democratic caucuses to be held after the polls close.

In an unusual system, the 193 delegates that Texas will send to the Democratic National Convention will be split between Obama and Clinton according to the results of both the primary and the caucuses.

State party officials say the dual primary/caucus system promotes participation in the party. Both Clinton and Obama have encouraged supporters to do the "Texas two-step" and vote in both events.

Obama came into the day with momentum on his side. He had 1,378 pledged delegates and superdelegates to Clinton's 1,269.

Neither candidate is close to the 2,025 needed to win the Democratic nomination.

Former President Bill Clinton said in February that if his wife won Ohio and Texas, she'd go on to win the nomination. E-mail to a friend

CNN's Paul Steinhauser, Rachel Stratfield, Mary Snow, Mark Preston and Sasha Johnson contributed to this report.

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