Rick Santorum said Monday that the odds for a brokered convention are "increasing," but remained evasive over whether he would get out of the race should it become clear he could not get to the 1,144 delegates needed to win.

"I think it's going to be very difficult as this goes on for anybody to get to that magic number," he told Charlie Rose of CBS's "This Morning." "What I'm going to do is continue to work hard to make sure there's a conservative who is the nominee of this party."

Santorum dodged a question on Sunday about whether he would step aside if no candidate won enough delegates going into the convention to clinch the nomination. If neither he nor Mitt Romney, who is currently leading in delegates, has the 1,144 required to lock up the race, the nomination could be decided at the Republican National Convention in August -- cutting the length of campaigning for the general election to only a few months.

Santorum said Monday that it would be easier to get to 1,144 if there were fewer challengers, alluding to Newt Gingrich and Ron Paul, both of whom trail him in delegates. He dismissed a question about whether Gingrich's continued presence in the race could help Romney to win the nomination, telling Rose, "I don't know how that all plays out."

"If the other people stay in the race, it's going to be hard for anyone to get to that magic number," he said. "We believe that if we get to the convention, Charlie, that the convention will nominate a conservative. They will not nominate the establishment moderate candidate from Massachusetts."