Losses in even one of the states could increase the pressure on her to drop out of the race as party support moves behind Obama.
"There will be people in her campaign who will argue a split decision is good enough to continue," said Cal Jillson, a political scientist at Southern Methodist University in Dallas.
"But as a practical matter, just looking at the delegates, the numbers won't really add up for her."
Obama acknowledged Clinton needs large wins in both states, which have a combined 334 delegates at stake, in an interview on ABC's "Good Morning America" programme.
"If we do well in Texas and Ohio, I think the math is such where it's going to be hard for her [Clinton] to win the nomination. And they'll have to make a decision about how much longer they want to pursue it," he said.
Clinton, though, remained upbeat.
"We think we are going to do really well here in Texas and Ohio,
I am feeling really optimistic," she said outside a school in
However the senator refused to speculate on her next move should the polls not favour her campaign.
"We are going to get through today, and we are going to see how we do. I believe in taking things one day at a time in politics, as in life."
Tuesday's contests could also put John McCain, the Republican front-runner, close to clinching his party's nomination.
McCain is favourite to beat his last remaining major challenger, Mike Huckabee, the former Arkansas governor, in all four states.
|Obama's appeal has so far won him 11|
consecutive state primaries [AFP]
Voting ends in Ohio at 7.30pm EST (0030GMT on Wednesday) and all voting in Texas will be over by 9pm EST (0200GMT on Wednesday).
Clinton and Obama made last-minute appeals for votes in Ohio and Texas on Monday.
Clinton was up before dawn to tour a car plant in Toledo, Ohio, and ending her day with a televised town hall meeting in Texas with time bought by her campaign.
She renewed her attacks on Obama over the North American Free Trade Agreement, an unpopular treaty in Ohio, which has suffered from manufacturing job losses.
Both candidates say the treaty should be renegotiated, but the Clinton campaign has highlighted reports that Austan Goolsbee, an adviser to Obama, assured the Canadian government that Obama's opposition was political rhetoric and not substantive.
Obama said Goolsbee had simply reiterated to Canadian officials his views on the treaty, and Canadian officials backed his version of the story.
The size of any win is important for Clinton as under Democratic rules the losers in each state still take a proportional number of delegates, meaning that unless Clinton wins by a large majority she will be unable to close the gap with Obama.