WASHINGTON (Reuters) - Hillary Clinton refused to count herself out of the U.S. presidential race on Tuesday as her hard-fought duel with Barack Obama for the Democratic nomination faced the judgment of voters in Ohio and Texas.

Turnout was expected to be strong in Ohio, Texas, Vermont and Rhode Island -- the states voting on Tuesday. Polls close in Ohio at 7:30 p.m. EST and all voting in Texas will be over by 9 p.m. EST.

First results could be available immediately after the polls close, although tight races could take hours to resolve.

Clinton, a New York senator battling to snap Obama’s string of 11 state-by-state victories, needs wins in both Ohio and Texas to rejuvenate her campaign and justify staying in the race until the next major contest -- Pennsylvania which votes on April 22.

Losses in either Texas or Ohio could set off a stampede of party support for Obama, raise pressure on Clinton to drop out and make it even tougher for her to cut Obama’s lead in the pledged delegates who will choose the Democratic nominee to contest November’s presidential election.

Tuesday’s contests also could put Arizona Sen. John McCain, the Republican front-runner, close to clinching his party’s nomination. McCain is favored to beat his last major rival, former Arkansas Gov. Mike Huckabee, in all four states.

“I believe that with your help today that we can secure enough delegates to make sure that we can secure the nomination, but we have to win and we have to win big here in the state of Texas,” McCain told supporters in San Antonio.

TIGHT RACES

Opinion polls show Clinton and Obama in close races in both Ohio and Texas -- the biggest prizes on Tuesday.

A cautious-sounding Obama told reporters on his campaign plane that he thought the race would be “very, very tight.”

“We started 20 points behind in Texas and Ohio,” he said on the flight from Houston to San Antonio. “We’ve closed the gap but whether it’s going to be enough to actually win is going to depend on what turnout looks like in both states.”

“What my head tells me is we’ve got a very sizable delegate lead that is going to be hard to overcome,” he added, when asked if the race would continue on through Pennsylvania.

The former first lady, who would be the first female U.S. president, refused to mull how she would respond to a loss.

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“I don’t think like that. We’re working hard,” Clinton told reporters. “We think we’re going to do really well here in Texas and in Ohio.”

Clinton had a slim lead in Texas over Obama, an Illinois senator who would be the first black president, and pulled even in Ohio, according to a Reuters/C-SPAN/Houston Chronicle poll released on Tuesday.

Obama noted that pundits have said Clinton must win Ohio and Texas in a landslide in order to make up for his 11-state streak. “I don’t think that’s going to happen,” he said.

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Clinton’s campaign aides have been tamping down expectations, easing away from talk that she needed to win both Ohio and Texas, with their combined 334 delegates.

Obama noted the stakes in a rally on Monday night.

“So here we are with the possibility of winning the nomination,” Obama said in Houston. “One of the things that I’ve learned is that what makes this powerful is not that things always go easy, but rather that we are willing to go forward when it’s hard.”

Like her husband, former President Bill Clinton, who nicknamed himself “The Comeback Kid” for his improbable rise to the White House in 1992, Clinton has dodged disaster before.

In January, Obama appeared ready to deal her a knockout blow in New Hampshire after his big win in Iowa, but she defied opinion polls and won.

After a landslide loss in South Carolina, Clinton battled Obama to a draw in Super Tuesday contests around the country on February 5, winning some of the biggest prizes of the night in California, New York and New Jersey.

Under Democratic rules allowing the losers in each state to win a proportional amount of delegates, Clinton cannot close the gap on Obama among pledged delegates unless she wins in Ohio and Texas by margins that appear beyond her grasp.

An MSNBC count gave Obama 1,194 delegates to Clinton’s 1,037 before Tuesday’s showdowns, well short of the 2,025 needed to win the nomination.

(Reporting by Ellen Wulfhorst, Caren Bohan and Jeff Mason in Texas, Writing by Deborah Charles, editing by Alan Elsner)