Senate Republicans should repeatedly offer bills to repeal health reform even if it's in vain, Sen. Tom CoburnThomas (Tom) Allen CoburnThe Hill's Campaign Report: Trump, Biden spar over coronavirus response Senator Tom Coburn's government oversight legacy Remembering Tom Coburn's quiet persistence MORE (R-Okla.) said Tuesday.

Coburn acknowledged efforts to repeal the legislation, or even defund it, were unlikely to be successful as long as President Obama is in the White House, but said making repeated efforts to dismantle the legislation is the best political strategy for the GOP.

"I think the best strategy is to call for a repeal bill and pass that bill," Coburn told a group of conservative bloggers. "And if you can't pass it the first time, then offer it again the next month, and offer it again the next month."

Republicans have publicly wrestled with how they might follow through with their pledge to repeal the healthcare bill Obama signed into law earlier this year. The GOP is poised to make major gains in Nov. 2's elections and is in position to win back the House and possibly the Senate.

Retiring Sen. Judd Gregg (R-N.H.), who's the top GOP member in the Senate Budget Committee, said last week that repealing the bill wasn't realistic and that Republicans should focus on retooling the new reform law instead.

Gregg's words rankled some conservatives, who worried the party will go soft on its promise to repeal health reform.

Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellOvernight Health Care: CDC recommends face coverings in public | Resistance to social distancing sparks new worries | Controversy over change of national stockpile definition | McConnell signals fourth coronavirus bill On The Money: Economy sheds 701K jobs in March | Why unemployment checks could take weeks | Confusion surrounds 9B in small-business loans 13 things to know for today about coronavirus MORE (R-Ky.) said that Senate Republicans are "committed" to seeing through with their pledge to repeal health reform.

"While we were unable to block the Democrats from passing the health spending bill—the single worst piece of legislation that’s passed since I’ve been in the Senate—the Republican leadership in the House and Senate is committed to its repeal," he said. "While Democrats will filibuster our efforts, and if we’re successful the President will veto, I believe we should give them that opportunity. We should vote, again, for repeal. Americans have spoken out, loud and clear, and we heard them. Repeal is part of the Pledge to America, and the Republican leadership is united in that effort.”

But even Coburn, one of the most conservative members of the Senate, acknowledged the Senate's procedural hurdles and that Obama's presence at the White House made Republicans' back-up plan of looking to defund parts of the bill unlikely.

"I would expect the president to veto any limitation of funds. It's highly unlikely that we would win a limitation amendment on an appropriation bill in the Senate, unless we saw a significant change of heart among Democrats," he explained, noting the filibuster rules requiring 60 votes to end debate on a measure. Even if Republicans win back a majority, they could have to convince as many as 10 Democrats to side with them on a repeal or defunding of the bill.

Coburn did predict some Democrats would have a change of heart, though he said it wasn't clear if it would be enough, even if Republicans achieve the most optimistic projections of Senate gains on Election Day.

"I think you'll see a significant change of heart with some of them," Coburn said.

Updated 1:12 p.m.