"Not only have we fought the good fight and finished the race but more importantly, we have kept the faith. I would rather lose an election than lose the principles that got me into politics in the first place," Huckabee said.
Clinton had the most at stake coming into the race, facing pressure to cede the nomination battle if she didn't win both Texas and Ohio, with a combined 370 delegates up for grabs.
Even former President Clinton said she must win both states to stay in the race, although a new ABC News/Washington Post poll shows Democrats by a 2-1 ratio think the former first lady should fight on even if she only wins one or the other.
Some influential Democrats suggested Clinton should drop out of the race if she wasn't ahead after Tuesday's votes.
"We have to have a positive campaign after Tuesday. Whoever has the most delegates after Tuesday, a clear lead, should be, in my judgment, the nominee," New Mexico Gov. Bill Richardson, a Democratic superdelegate, said on CBS' "Face the Nation" Sunday.
Hispanics turned out in big numbers in the Texas Democratic primary, accounting for a record 30 percent of voters, up from 24 percent in 2004, according to preliminary exit poll results.
Hispanics went 63 percent to 35 percent for Clinton over Obama. Clinton also won white women in Texas by 19 points while white men split evenly between Clinton and Obama. The Illinois senator won 85 percent of black voters in Texas, who accounted for 19 percent of Democratic primary voters in the Lone Star State.
Many Texans took advantage of early voting rules; early voting is expected to account for 50 percent of the total Democratic primary votes, according to the Texas Secretary of State's office.
But earlier Tuesday Clinton expressed dismay at the peculiar voting rules in Texas, where Democratic delegates are allocated through a combination of the results from primary votes and caucuses. Texas apportions delegates in a complex system that may yield Obama more delegates from expected wins in Texas' big cities, while giving Clinton less delegates for expected wins in Latino areas along the border.
"When the dust clears, we have to ask some tough questions," Clinton told reporters in reference to the Texas voting rules, arguing that the limited window to appear at a caucus makes it difficult for particularly working class voters to participate.
Obama went into Tuesday's contest with a 110-delegate lead, according to the ABC News delegate scorecard.
Clinton has a very serious math problem. Almost regardless of what happens Tuesday and in the few remaining states left to vote, she will be behind Obama in delegates when the last primary vote is cast in Puerto Rico in June. That makes the role of superdelegates all the more important.
The Obama campaign issued a statement Tuesday suggesting Clinton must make a significant dent in Obama's pledged delegate lead -- an unlikely event given state polling and the Democratic Party's proportional system for according delegates.
On Tuesday the Clinton campaign accused the Obama campaign of Election Day chicanery in Texas, an accusation the Obama campaign denied.