Hagle said Romney must make conservative voters more comfortable with him.
"That's really the fundamental problem Mitt has," he said. "With Romney, you may get the feeling he's more detached. … I believe what he says, but I can see where a lot of people might say, 'We're not sure. We'd like to see more passion.'"
Some congressional Republicans have sent a similar message to Romney this week, complaining to Politico that he's been playing it too safe and should see Tuesday's results as a signal he needs to make a shift.
Sen. Mike Lee, R-Utah, shared their concerns that conservatives in the party want to know who the nominee will be "sooner rather than later" but acknowledged that might be wishful thinking.
"The Santorum victories this week did have an impact on what was becoming a real sense of inevitability behind Mitt," Lee said. "I don't think conservatives are going to coalesce behind one candidate until there's an heir apparent."
Lee, seen as a tea party leader, has not endorsed a presidential candidate and doesn't plan to, choosing to use his clout to back Senate contenders in key races.
The presidential race, he said, "is still up in the air. There is no consensus among conservatives who is the best candidate for conservatives. Each of the remaining candidates has made a persuasive case why he's the guy."
Lee said he trusts that "whichever man comes out on top is going to be the man who's best equipped to beat Obama." He said he expects Romney to be the nominee.
"I'm not 100 percent certain of it, but I do think it's going to be likely," Lee said, predicting that by April, Romney could be in a position to claim the nomination.
He said if Romney becomes the nominee, he "absolutely" will have the support of conservatives. "I think Mitt Romney is a true conservative," Lee said. "Conservatives are not going to have a problem getting behind him."
Romney's campaign is now focused on winning the next primary states to vote, Arizona and Michigan on Feb. 28, and the Super Tuesday races that follow on March 6.
"Santorum has had difficulty in states where a lot of people vote, that require a broader outreach," said Kirk Jowers, a longtime Romney supporter and head of the University of Utah's Hinckley Institute of Politics.
Jowers said it's not clear who is Romney's chief rival is going forward.
"I think this it's a very legitimate question," he said. "Santorum and Gingrich have each had some victories and some colossal no-shows. Neither of them has shown the ability to mount a sustained campaign against Romney."
Chaffetz said Romney is still the candidate to beat.
"You look at the vote totals," the congressman said. "Slice them and dice them any way you want, Mitt Romney has been dominating."
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