(CBS News) After bowing out from the Republican presidential race Wednesday, former House Speaker Newt Gingrich is no worse off than he was before he ran for president, says CBS News chief Washington correspondent Bob Schieffer. Mitt Romney, on the other hand, will likely have to deal with some of Gingrich's less-than-complimentary "sound bites" about him for the remainder of the campaign.
"Gingrich knew from the very beginning that this was a long shot, but he also knew what a lot of other Republicans know, that there are many, many Republicans on the right side of the party who simply don't like Mitt Romney, who don't believe that he is one of them, a true conservative," Schieffer told Charlie Rose Thursday on "CBS This Morning."
The candidate spent months on the campaign trail attempting to stake his claim as the true conservative in the race. Even as it became clear he would not be able to assume that mantle -- in part because he was vying against Rick Santorum for the title -- Gingrich vowed to stay in it until the Republican convention this summer. But facing millions of dollars in campaign debt and with just two Republican primary victories under his belt, Gingrich, suspending his campaign for the presidency so he could go back to being an "active citizen."
"Gingrich thought if he could build on [conservative Republicans] as the base, as a sort of 'anybody but Romney' candidate, that slowly but surely he'd have a chance," Schieffer told Rose. "But as it turned out, he didn't."
Instead, Schieffer said, Romney used his significant financial advantage to hammer his opponents with negative ad campaigns.
Still, "I don't think he's hurt himself," Schieffer said, of the former speaker.
"He got a lot of exposure. And he'll continue to do what he was doing before he ran. That is to give a lot of lectures, write books, and so on."
Romney, on the other hand, is going to have to deal with the fallout of the long, tough Republican primary battle for months to come.
"I think this Republican primary was just soundbite heaven for Democrats," Schieffer said. "I mean, they recorded all of this. And you're going to hear not only what Newt Gingrich said about Mitt Romney as the campaign continues on, but what the rest of them said as well."
"I think that Mitt Romney's going to have to deal with this," he added.
To see the Schieffer interview, click on the video in the player above.