As such both Rubio and Cruz, who are competing to gain the number two spot in now the five-person GOP presidential race, claimed they would have the support of majority of the party's members and thus emerge as the GOP nominee.
"Majority of Republican voters are not supporting Donald Trump. Obviously, once this race begins to narrow a little bit, you'll see more of that support consolidating," Rubio said at a Fox News organised town hall in Houston, Texas.
"I relish that. This is a country of underdogs. This is a nation made up of people who scratch and claw to move ahead and improve their lives. And this an important election," he said.
"We are not going to allow the conservative movement to be defined by a nominee who isn't a conservative. We certainly need to elect someone who's prepared to be president in a thoughtful and serious and important way, given the threats this country faces," Rubio said.
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Appearing at the same town hall, Cruz said Trump has a lot of momentum right now.
"In my view you look nationally, anywhere from 65 to 70 per cent of Republicans don't think Donald is the right candidate for us to nominate to go up against Hillary Clinton," he observed.
"If you're among those 65, 70 per cent of Republicans that think Donald is the wrong choice, then Super Tuesday is the opportunity for us to coalesce behind our campaign because we're the only campaign in a position to beat him," Cruz said.
"They're furious with Washington. They're furious with politicians in both parties that have been lying to them. And I think Donald support is a manifestation of that," he said.
"I think he has a fairly low ceiling, I think it's 35 to 40 per cent. A majority of Republicans don't think he's the right nominee. If you look nationally, in the head-to-head polls, Donald consistently loses to Hillary. I consistently beat Hillary," he said.
"So the question right now is, how do we prevent nominating a candidate who loses the general election or for that matter, if Donald wins the general election, who the heck knows what he will do as president? I mean, you know, we need a president we can trust," Cruz said.