Twenty hours after declaring his candidacy for the presidency, Senator Ted Cruz is seeing “breathtaking” energy on the campaign trail, he said in an interview on Tuesday morning.

“The energy and exhilaration there yesterday and we’re seeing on the trail, it takes your breath away,” Cruz said in an appearance on NBC’s Today show, alongside his wife, Heidi.

It was unclear what trail stops Cruz was referring to. Following the announcement of his candidacy on Monday at a Liberty University event at which student attendance was mandatory, Cruz returned to Washington to make an appearance on Fox News.

Sniping among Republican competitors for the 2016 presidential nomination heated up late Monday, with Senator Rand Paul slipping on to Fox News ahead of Cruz to poke fun at the fact that Cruz had launched his presidential campaign at an event with required attendance.

Paul, who is expected to declare his own candidacy within weeks, was asked about a group of students at the event who stood behind Cruz wearing red “Stand with Rand” T-shirts. Paul said his team had not arranged the tableau.

“I’m not sure who did orchestrate it,” Paul said. “But I kind of remember those days, because I went to Baylor University, and we were all required to go to convocation. So all these kids were required, and some of those who were required wanted to make sure that just by having to be here, they weren’t expressing their support.”

Paul suggested that Cruz, who is campaigning on a platform of abolishing the IRS and repealing “every word” of Barack Obama’s healthcare reforms, was “throwing out red meat” to the conservative base without reaching out to the moderate voters who will be crucial to general election success.

“If you look at our voting records, you’ll find we’re very, very similar,” Paul said of Cruz. “I guess what makes us different is probably our approach as to how we would make the party bigger. And I’m a big believer that you should stand on principle and be true to your principles, but I also think that we should take those principles and try to bring in new people with them.”

In his Today show appearance, Cruz rejected the notion that he was an intransigent extremist whose unbending positions in the Senate had made him an enemy of compromise – the most glaring evidence of which, his critics say, being the partial shutdown of the federal government he helped precipitate in October 2013 with a profoundly feckless attempt to block the president’s healthcare law.

“I’m perfectly happy to work with anyone: Democrat, independent, libertarian,” Cruz said, “if they’re shrinking the size and power of the federal government, shrinking the debt and expanding liberty.”

Asked about the secret Ted Cruz the public does not see, Heidi Cruz did not refer to a hidden penchant for compromise but to Cruz’s sense of conviction.

“It was one of the things that really drew me to him, is that this is a person with conviction,” said Heidi, who has taken leave from her job as a managing director at Goldman Sachs Group Inc to help the campaign.

Cruz, a champion debater in his college years with a distinguished record of arguing cases before the US supreme court, argued in his Hannity appearance against the idea that he was too radical to be electable. Cruz specifically set his sights on an analysis published on Monday by the data journalism website FiveThirtyEight, which Cruz incorrectly referred to as being part of the New York Times, a bugbear for the Fox News audience.

FiveThirtyEight split with the Times two years ago, when founder Nate Silver moved the enterprise to ESPN/ABC News. On Monday the site’s senior political writer, Harry Enten, formerly of the Guardian US, published a piece called “Let’s Be Serious about Ted Cruz from the Start: He’s Too Extreme and Too Disliked to Win.”

“You know, Sean, when the New York Times says the Washington elites despise me, my only question is whether I have to disclose that to the [Federal Election Commission] as an in-kind donation,” Cruz said. “I can’t think of a better ground to run on.”