GOP presidential hopefuls Newt Gingrich and Rick Santorum today trumpeted their chances of winning upcoming primaries in Alabama and Mississippi, but both face a basic delegate math problem to catch up to frontrunner Mitt Romney.

Gingrich, a former Speaker from Georgia, predicted victory in the two states, saying on “Fox News Sunday,” “I think we’ll win both.” But he stopped short of saying that Mississippi and Alabama are must-win contests, as some aides have suggested.

Gingrich has said that he will remain in the race through the Republican National Convention in Tampa, Fla., in August, but he declined to say on Fox News whether he would leave the race if Tuesday’s primaries don’t turn out as he predicts. American Samoa and Hawaii also hold caucuses Tuesday.

Santorum also voiced optimism about Tuesday’s contests on “Meet the Press” today, saying, “We’re out there running an insurgent campaign, and we feel good.”

But the former Pennsylvania Senator added: “It’s a pretty tough battleground out there. I’m in Newt’s backyard.” Gingrich won the GOP primaries in South Carolina and Georgia, and has played up his appeal to Southern and evangelical voters.

Santorum said if he could “get a one-on-one” race with Romney, he could “do very well,” but he stopped short of saying that Gingrich should withdraw. A pro-Santorum super PAC, the Red White and Blue Fund, has called on Gingrich to drop out. Asked why he does not do the same, Santorum responded: “I didn’t ask Speaker Gingrich to get in, I’m not going to ask him to get out.”

Both Santorum and Gingrich suggested that Romney may have trouble collecting the 1,144 delegates that he will need to win the nomination.

“Romney needs about 50 percent of the delegates” to meet that target, Santorum said. “On the current track we’re on right now, Romney doesn’t make that projection.” Santorum noted that he’s been outspent 10-to-1, but is heading into “great states” such as Pennsylvania, his home territory, and Texas, where he maintained that polls show him with a sizable lead.

“We’ve got the grass-roots support,” he added. “We’ve been slowly crawling our way back into this race, and we’re in a great position right now going forward, with states that are very favorable to us, in very favorable areas of the country.”

Even delegates who have voted for Romney “are not bound by their commitment,” Santorum said, hinting that the Tampa convention could hold surprises.

Gingrich also suggested on Fox that Romney may not reach the magical number of 1,144. If that happens, he said, the GOP would begin a “60-day conversation” about what comes next.

But Romney has 454 delegates, according to the latest Associated Press tally, more than all his rivals combined, following contests Saturday in Kansas, Wyoming and three U.S. territories. Santorum came out ahead in Kansas, while Romney took Wyoming. Santorum now has 217 delegates, by the AP’s count; Gingrich has 107, and Rep. Ron Paul (R-Texas) has 47.