The candidates also tried to appeal to Hispanics -- a large portion of the Texas electorate -- by stressing their support for immigration reform and highlighting their work on legislation to help immigrants and their families, The Washington Post (NYSE:WPO) reported Friday.

Thursday's debate at the University of Texas's Austin campus is the first of two before the March 4 primaries in the Lone Star state and Ohio, Vermont and Rhode Island. The two debate Tuesday in Cleveland. Clinton has seen her lead fade while Obama's campaign has gained momentum, capturing all voting events since Super Tuesday.

Reacting to Fidel Castro's resignation as Cuba's president, the two debated policy regarding the island nation, which the United States has boycotted for decades, and whether they would meet the new leader without preconditions. Clinton said no and Obama said yes, but he added that he would do so only with plenty of preparation.

Regarding healthcare, Clinton said her plan would require all people in the United States to buy into a universal healthcare plan. Obama would not have such a requirement, but said his plan would make health insurance affordable.