(CNN) -- Sen. Hillary Clinton claimed victory in Ohio, a state considered a must-win for her campaign.
Sen. Hillary Clinton is projected to score a big win in Ohio.
Clinton earlier broke Barack Obama's 12-contest winning streak with her victory in Rhode Island.
"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 was projected to take Vermont, but the contest in Texas was too close to call.
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.
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. Video 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 until 9 p.m. ET.
In Texas, Clinton holds a two-to-one advantage over Obama with Hispanic voters, while Obama has 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
These early surveys provide a snapshot of the race, but are not conclusive on who will win the critical contest.
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.
Obama appeals most strongly to younger voters while older voters favor 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 leads Obama 67-31 percent.
The same pattern holds true in early exit polling from the Texas Democratic primary. Among voters aged 18 to 29, Obama leads Clinton 61-39 percent, and among voters 60 and older, Clinton leads Obama 63- 36 percent.
Steady streams of people cast ballots in Tuesday's contests, and officials in the delegate-rich states of Ohio and Texas said they expect record turnouts.
Despite freezing rain in northern Ohio and bad weather elsewhere in the state, Ohio Secretary of State Jennifer Brunner estimated that as many as 52 percent of registered voters might go to the polls, 15 percentage points higher than the average of past presidential primaries.
Three polling stations in Jefferson County in eastern Ohio were relocated Tuesday because of flooding that could have prevented people from voting, election officials said.
County residents unable to get to their designated polling places because of bad weather were given the option of casting provisional ballots Tuesday in Steubenville, the county seat, at the offices of the Board of Elections, officials said. The board has to verify those ballots by March 25. Photo See scenes from Tuesday's voting »
I-Reporter Bruce Goldberg reported long lines at the polls in Grapevine, Texas. When he voted at 7:20 a.m., he said 70 people had already voted in the Democratic primary.
"There's usually a big line of Republicans and nobody at the Democratic table at the primary," he said. "When I walked in this morning, there were a lot of cars out, and it was the complete opposite."
Poll workers in Collin County, near Dallas, also reported high turnout for the Democratic primary. The Dallas Morning News called Collin one of the most Republican counties in the state.
Poll workers there 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 comes into the day with momentum on his side. He has 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. Clinton and Obama will be competing for 370 delegates Tuesday. Texas and Ohio, which has 141 delegates, will be the biggest prizes. Allocate delegates yourself and see how the numbers add up »
Former President Bill Clinton said in February that if his wife wins Ohio and Texas, she'll go on to win the nomination. Whether she will drop out of the race if she doesn't win either of those states is another question.
While visiting a polling station in the mostly-Latino east end of Houston on Tuesday morning, Clinton said she felt "really good about" Tuesday's elections and was expecting "tremendous" turnout across Texas.
Clinton did not make a prediction about the outcome of Tuesday's races, but her campaign chairman, Terry McAuliffe, was not so guarded Tuesday morning. He predicted Clinton wins in both Texas and Ohio.
"I've said this for a long time. These are two big states," he told CNN. "There's a lot of big issues: national security, the issues on the economy. Those are Hillary's issues. She's been out front in the polling data on all of those."
CNN's poll of polls, an averaging of the most recent surveys in each state, suggests the race is extremely tight, with Obama ahead by 2 points in Texas and Clinton ahead by 5 in Ohio. But the polls also indicate there are still many undecided voters in both states.