Armey told CNN's "State of the Union" he does not think Gingrich can replicate his South Carolina upset of front-runner Mitt Romney in other states.
"I think he has played that string out," Armey said. "In the meantime, Mitt continues to work along at a steady pace, and we are left with a dilemma that we are not going to get a reliable, small-government conservative out of this nominating process."
Armey said he believes the Tea Party crowd could get behind Romney, a former governor of Massachusetts, despite his seemingly moderate stances, and would count on Republicans in Congress to drive the conservative agenda.
"Our notion is, we will get the legislative initiative coming out of a conservative-dominated House and Senate," he said.
Gingrich, a former House speaker from Georgia, predicted he would indeed pick up steam in February by unveiling "bold" initiatives on thorny issues such as welfare, Social Security and taxes that would distinguish himself from Romney, who he called "not very distinguishable from" President Obama.
"My goal is to show there is a way to change Washington that is different from Obama and Romney," Gingrich said.
Despite losing more ground to Romney and Gingrich in the Florida and Nevada contests, the two dark horses told the Sunday news shows they are still in the race.
Santorum predicted the Romney-Gingrich victory streak could become breakable as the campaign slogs on since the two leaders will be getting into relatively unknown territory compared with the early primary states.
"The first five states were sort of cast in stone," Santorum told "Fox News Sunday."
"Now, we are getting to the states where people don't have the natural advantage, don't have the time commitment, the staff commitment to really build out an organization like they did in these first five," Santorum said. "I think we're going to do very well here in Minnesota. I think we're going to do very well in Colorado, and we've got a one-on-one match-up against Mitt Romney in Missouri."
David Axelrod, a top Obama adviser, agreed with Santorum, telling NBC's "Meet the Press" he already sees Romney losing steam.
"I believe this will go on for a while," he said.
"Independent voters are fleeing Governor Romney now and his numbers are falling," said Axelrod, who needled Romney for supposedly "pandering" to the right wing of the GOP. "He's underwater nationally."
Paul, who has failed to post any wins despite a dedicated base of supporters, admitted he couldn't predict when or if he would win a primary; however, he would continue on to Colorado and Minnesota, which hold their Republican caucuses Tuesday.
Paul told ABC's "This Week" Romney in particular would have to work to secure the support of Paul voters, particularly by adopting more of Paul's economic ideas.
"I think Mitt can change his mind," Paul said. "He's changed his mind in the past and if he hears from our young people and voters, then yeah, he's going to change his mind, if there's a political benefit to it."