"This time we have a lot more name recognition. That's helpful," Love said. "We have a great campaign staff. We have got people who know how to do this. And we're going to be getting out and reaching as many people as possible."
Matheson countered, saying that, having represented the district for two years now, he is confident voters will re-elect him.
"This time she's got to stand on her own two feet," Matheson said. "She doesn't get to stand on the huge coattails of Mitt Romney."
Love would still have to win the Republican nomination next year to set up the Matheson showdown, but she has been aggressively raising money and lining up support from Utah's GOP establishment.
West and Love took repeated swings at the Affordable Care Act, commonly known as Obamacare.
West said people are wrong to resign themselves to Obamacare being "the law of the land," and Love responded, "Slavery was a law of the land too, right? That doesn't mean it shouldn't be changed."
She said 5.2 million Americans have lost their insurance policies as a result of the change because the existing policies don't meet the minimum coverage requirements of the new law and figures released Wednesday show only about 106,000 have signed up for new coverage.
West said Republicans need to be smart in responding.
"The most important thing for the Republican Party is not to gloat and not to go out there and say, 'I told you so,' " he said, but instead "be the one who solves this thing."
He suggested enacting targeted subsidies and high-risk pools to cover those who can't get insurance, working with the insurance companies to get coverage for those whose policies were canceled, and expanding health-savings accounts.
Love was asked several times whether she would have voted for the budget bill that ended the federal government shutdown resulting from an impasse in Congress over whether to fund Obamacare, but wouldn't answer, calling the question a hypothetical.
"I support trying to defund [it]. I support trying to get rid of the Affordable Care Act," she said. "The problem with the way everything went is shutting down the government didn't touch the Affordable Care Act."
Love said Matheson should have met with constituents before voting to restore federal funding to the government.
"He should have faced his residents, face to face, to figure out how they wanted him to vote," she said.
Matheson said the criticism is laughable.
"I was stuck in Washington because of the shutdown," he said, "but, secondly, I heard from thousands of constituents, phone calls, emails saying, 'Stop this nonsense.' "
Matheson also said it is telling that Love brought West to Utah, adding that his ideas are far outside the mainstream "and so is she."
"He is the poster boy of what's wrong with politics in America. He's reckless, he's irresponsible and if there are people who don't agree with him, he calls them names," Matheson said. "I think birds of a feather flock together. If she wants to be associated with Allen West, more power to her."
Love praised West's convictions, although she distanced herself somewhat on style, particularly some inflammatory comments he has made for example, suggesting Democrats in Congress were communists and calling President Barack Obama a tyrant.
She said candidates can agree on values and differ on style and their message.
West has started an organization called the Guardian Fund, created to help elect conservative military veterans and minorities to Congress.
West noted that he had the opportunity to pose for a picture with Love and Utah GOP Chairman James Evans, all three of whom are black, which West said was historic. If she is elected, Love would be the first black Republican woman in Congress.
"Think how powerful that image is, because you did not bring us to these positions because of the color of our skin. You allowed us to have these positions because of the content of our character," he said. "That is what makes us different from the Democratic Party."