Updated

Sen. Bill Cassidy fired back Thursday at late-night talk show host Jimmy Kimmel, as their feud over the health care bill the Louisiana Republican senator has co-authored extended into a third day.

“Jimmy doesn’t understand,” Cassidy told “Fox & Friends.”

The host of ABC's “Jimmy Kimmel Live,” who delivered a memorable monologue in May when he revealed his newborn son’s heart condition, first took aim at Cassidy and his bill on Tuesday night. He said Cassidy “was not very honest” in an earlier appearance on his show.

Kimmel said Cassidy coined the term, "the Jimmy Kimmel test," which was summed up by Kimmel as: No family should be denied medical care, emergency or otherwise, because they can’t afford it. They agreed the test would mean no lifetime caps, Kimmel said.

Kimmel claimed, “This guy, Bill Cassidy, just lied to my face.”

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The host doubled down Wednesday night, again accusing the senator of breaking a vow to oppose plans that allow insurers to turn back people with pre-existing conditions.

But Cassidy said Thursday that his legislation, which he and Sen. Lindsey Graham, R-S.C., introduced, would “absolutely” be cheaper and better than ObamaCare.

'He’s only heard from those on the left who are doing their best to preserve ObamaCare.'

— Sen. Bill Cassidy, R-La., referring to Jimmy Kimmel

“Jimmy doesn’t understand, not because he’s a talk show host -- because we’ve never spoken,” Cassidy said. “He’s only heard from those on the left who are doing their best to preserve ObamaCare. He’s not heard from me, because we’ve not spoken.”

The senator has spoken to Kimmel; he appeared on Kimmel’s show back in May. Challenged on that point, Cassidy acknowledged he was on the show but seemed to say that he and the host have not spoken specifically about his latest bill, which he said would give millions to the states to help low-income families get access to insurance and care for pre-existing conditions.

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Amid the feud, the White House is trying to rally support for the legislation in hopes of a possible Senate vote next week.

“This may well be our last best chance” to pursue health care reform based on “individual choice” and “state-based innovation,” Vice President Pence told “Fox & Friends” on Thursday.

He added, “We have to recognize that ObamaCare has failed.”

At its core, the bill would put ObamaCare’s financing for subsidized private health insurance and Medicaid expansion into a giant pot and redistribute it among states according to new formulas.

States could obtain federal waivers allowing them to modify insurance market safeguards for consumers. This means states could set their own coverage requirements. The bill also would allow insurers to boost prices on people with serious medical conditions, end former President Barack Obama's mandates that most Americans buy insurance and that companies offer coverage to workers, and cut and reshape Medicaid.

The bill's full impacts are difficult to predict because the Congressional Budget Office has not had time to assess it.

The Associated Press contributed to this report.