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HOUSTON (AP) -- Barack Obama sought a knockout against rival Hillary Rodham Clinton as voting began Tuesday in crucial contests in Texas and Ohio, where the former first lady desperately needs a win to salvage her once-powerful candidacy for the Democratic presidential nomination.

Both expressed confidence in their chances the previous night, which they spent in the same Texas city. But both teams also acknowledged that split decisions and close votes could prolong the battle for at least another month -- or more.

''We know this has been an extraordinary election. It continues to be. We're working hard to do as well as we can,'' said Obama, who planned to await Texas returns in San Antonio.

''I'm just getting warmed up,'' Clinton told reporters, a clear sign that she expects to press the campaign on beyond Tuesday no matter the outcome.

She planned to opening Election Day in Houston and Dallas, but then head back to Ohio for more campaign events. She will await results in Columbus before returning to Washington Tuesday night.

Polls show tight races in both Texas and Ohio. The Obama campaign saw Texas as their best opportunity, while the Clinton campaign saw Ohio as theirs. Texas offers 228 delegates, Ohio 164.

''Your voice can win an election,'' Obama told a noisy late-night rally in Houston. Repeating a signature election refrain, he shouted: ''I have only one question for you: Are you fired up? Ready to go?'' When the crowd roared its approval, he added: ''Let's go change the world.''

His wife, Michelle, had a more subdued message for the cheering supporters: ''We have a lot of work to do.''

Obama spent Monday campaigning in Texas, emphasizing his readiness to take over as commander in chief.

But he was dogged by allegations that he had overstated his opposition to the North American Free Trade Agreement to win votes in Ohio; and his ties to Chicago businessman Antoin ''Tony'' Rezko on the day that jury selection began in the political corruption trial of the real estate developer and fast-food magnate.

''Tony Rezko was a friend and supporter of mine for many years. These charges are completely unrelated to me, and nobody disputes that,'' Obama said at a news conference in San Antonio.

Obama did receive a $10,000 contribution made by a Rezko associate that is mentioned in the indictment. But Obama's campaign has long since sent the money to charity.

''There's no dispute that he raised money for us, and there's no dispute that we've tried to get rid of it,'' Obama said.

Meanwhile, Clinton waged yet another marathon day on Monday, shaking hands in the chill pre-dawn darkness with workers at a Chrysler factory in Toledo and winding up in Texas. She predicted a strong showing in the primaries and said she was looking ahead to contests down the road like Pennsylvania on April 22.

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