"If Leader McConnell can get us across the finish line in a combined repeal and replace, I'd like to see that happen," the Republican freshman senator said in an interview with Jake Tapper on CNN's "State of the Union." "It needs to be a good replace, but if we can do a combined repeal and replace over the next week that's great. If we can't, though, then there's no reason to walk away. We should do repeal with a delay let's be clear, I don't want to see anybody thrown off the coverage they have now. I would want to delay so that we can get straight to work."

Sasse first suggested the option of repealing and then replacing the Affordable Care Act, President Barack Obama's signature health care law, in a letter to President Donald Trump on Thursday an idea that Trump also voiced, but was met by criticism from both Republicans and Democrats who worried that it could harm Americans by leaving them without coverage.

"On July 10, if we don't have agreement on a combined repeal and replace plan, we should immediately vote again on H.R. 3762, the December 2015 ObamaCare repeal legislation that the Congress passed but President Obama vetoed," Sasse wrote in the letter. "We should include a year-long implementation delay to give comfort to Americans currently on ObamaCare that a replacement plan will be enacted before expiration."

Later that day, Trump tweeted, "If Republican Senators are unable to pass what they are working on now, they should immediately REPEAL, and then REPLACE at a later date!"

Vermont Sen. Bernie Sanders countered Sasse's argument on Sunday, calling the "repeal and then replace" option "absurd."

"I have a lot of respect for Sen. Sasse, but that idea is an absurd idea," the independent senator said in an interview on "State of the Union."

Republican Rep. Adam Kinzinger of Illinois has also rejected the suggestion of repealing and then later replacing the law, saying it could harm Americans.

"I think it's repeal and replace," Kinzinger told CNN's Chris Cuomo Friday on "New Day." "We can argue whether they like the system we're bringing them in or not, but simply a repeal, even with the sunset the year or two down the road -- the problem (is) we know how Washington works."

Sasse cast doubt on the CBO report Sunday, saying that "(r)egularly, government scorekeepers underestimate cost and they overestimate coverage."

"CBO is filled with lots of well-meaning people, and they're good at certain kinds of analysis, but analyzing macro long-term, highly complex, dynamic social programs, thev're almost never been right," Sasse added.

The current Republican plan in Congress is to do both a repeal and a replacement of the law in one massive piece of legislation, though the Senate's bill has struggled to gain the necessary GOP support.

"I think we need to do both repeal and replace, and I'm a little agnostic as to whether they're paired or separated," Sasse added in his "State of the Union" interview on Sunday, calling for the cancellation of the Senate's August recess so lawmakers can get to work on a replacement plan.

Senate Majority Leader Mitch McConnell said Friday that he will stick to the path of accomplishing both a repeal and a replacement together.

Finding a replacement for the law is "very challenging," but allowing Obamacare to remain in place is not an option, McConnell said, according to a video of his remarks posted on the website of the Courier-Journal newspaper, based in Louisville, Kentucky.

"We think that Leader McConnell and his senators within the Senate are working to try to get this piece of legislation on track," Price said. "Their conversations are ongoing as we speak, so we look forward to hopefully them coming aback after this 4th of July recess and getting the work done."

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Sasse: 'Repeal with a delay,' then replace - CNN