Hillary Clinton is showing no signs of letting up on her quest to seek the Oval Office, despite 11 straight primary battle losses and now-razor-thin support in the two states she needs a win from -- Texas and Ohio -- which began voting Tuesday morning.

Clinton's campaign advisers are looking beyond Tuesday's contests, which also include Rhode Island and Vermont, to the remaining 16 states that have yet to pick their nominee. The biggest prize among those is Pennsylvania, which votes April 22.

Click here to read FOX News Correspondent Major Garrett's blog about why many Democrats say the primary contest won't be over on Tuesday night.

After that, if Clinton continues on, the race continues on to Denver, the site of the August Democratic convention.

"I'm just getting warmed up," Clinton told reporters Monday, telegraphing her intent to push on after this week.

But chief rival Barack Obama is looking to land a knockout punch on Clinton.

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.

Most polls showed Clinton and Obama locked in a statistical dead heat in both Ohio and Texas, but one poll showed a preference by Democrats for Clinton to remain in the race if she wins at least one state on Tuesday.

The Washington Post poll released Tuesday said only 29 percent of Democrats think Clinton should leave the race if she loses either Texas or Ohio, but her support quickly erodes if she loses both states: 51 percent say she should quit in that case.

Clinton planned to open 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.

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 sounded a populist economic theme as she courted voters who have suffered with the decline of manufacturing in the industrial Midwest and Ohio. Then, in military-friendly Texas, Clinton broadened her theme to include veterans' issues and to trumpet her backing from a string of top military officers.

Clinton worked to underscore her core campaign theme that she's the more experienced on the issue. She held a one-hour town hall meeting where she strode the stage surrounded by a friendly audience and took questions selected from the thousands that were submitted on issues ranging from health care to education to veterans issues. Her campaign purchased time on a sports-oriented cable network to broadcast the event around the state, and the event was streamed on the campaign's Web site.

Both Clinton and Obama launched new television spots in Texas and Ohio to make their closing arguments.

Clinton ended her day with a rambunctious rally in Austin before flying to Houston.

Obama campaign manager David Plouffe called Tuesday "the last big window of opportunity" for Clinton, noting that "enormous leads" she enjoyed as recently as two weeks ago had dwindled or evaporated.

Still, he said Obama was mindful that "this could go on for some time. We're prepared for whatever situation occurs."

Republican presidential contenders John McCain and Mike Huckabee also campaigned in Texas, though voter interest centered on the closer Democratic race.

The Associated Press contributed to this report.