Senate Republicans say they would like Arizona Gov. Doug Ducey (R) to appoint a successor to the late Sen. John McCain John Sidney McCainAnalysis: Biden victory, Democratic sweep would bring biggest boost to economy The Memo: Trump's strengths complicate election picture Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ariz.) who, unlike McCain, would support GOP legislation to repeal ObamaCare.

Republican lawmakers say they won’t have time to hold another vote to repeal the law in 2018 but vow to try again next year if they manage to keep their Senate and House majorities.

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Sen. Ron Johnson Ronald (Ron) Harold JohnsonThe Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' The Hill's 12:30 Report: Ginsburg lies in repose CHC leaders urge Senate to oppose Chad Wolf nomination MORE (R-Wis.) said he hopes the next senator from Arizona will be a “strong ally” who “recognizes that ObamaCare is not a proper solution.”

“It hasn’t worked. It’s created a lot of harm and damage to real people,” he added.

A senior Senate GOP aide said the chamber would “absolutely” vote again to repeal ObamaCare but cautioned it would depend on “if we keep the House.”

“McCain was personally conservative but ideologically inconsistent,” the aide said. “I think Ducey is going to pick someone more like himself. He’s a more reliable conservative.”

McCain’s surprise vote to reject legislation that would repeal core pillars of the 2010 Patient Protection and Affordable Care Act — also known as ObamaCare — was the most impactful decision of his final year in the Senate.

It quashed the GOP’s eight-year quest to repeal the law and forced party leaders to drop major health-care legislation for the rest of the 115th Congress.

McCain’s vote remained a point of contention with President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE for months afterward.

The president mocked McCain at a Nevada rally in June for voting "no" on the repeal measure with a thumbs-down gesture.

The vote caught Trump and GOP leaders completely by surprise.

“Nobody knew he was going to do that. He campaigned on repeal and replace,” Trump told the Nevada audience. “Nobody talked to him. Nobody needed to, and then he walked in: thumbs down.”

More generally, GOP senators say they would like the new senator from Arizona to have a better working relationship with Trump.

“I think it would serve a useful purpose to get along with the president,” Sen. James Inhofe James (Jim) Mountain InhofeChamber of Commerce endorses McSally for reelection Overnight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Top admiral: 'No condition' where US should conduct nuclear test 'at this time' MORE (R-Okla.) said. “By having a sincere appreciation, admiration and respect, you can get a lot more done than [by being] adversarial.”

“It’s hard to imagine he could pick anyone more antagonistic,” quipped a GOP senator who requested anonymity, referring to Ducey.

Republican senators say they don’t want similar surprises from McCain’s successor

“I’d love to have somebody to take care of that,” Sen. David Perdue (R-Ga.) said of repealing ObamaCare.

Republicans repealed a main component of ObamaCare last year when they eliminated the law’s requirement that individuals obtain health insurance or pay a fine.

But GOP lawmakers say they can do more.

“Can we make insurance more affordable? Absolutely,” said Sen. Bill Cassidy William (Bill) Morgan CassidyCoushatta tribe begins long road to recovery after Hurricane Laura Senators offer disaster tax relief bill Bottom line MORE (R-La.). “More needs to be done.”

Cassidy said he doesn’t know whether the Senate will move another comprehensive health-care reform package, but he expects Republican leaders will push “piecemeal efforts to make affordable once more that which has not been affordable since ObamaCare passed.”

GOP senators think they have a good chance to increase their Senate majority because Democrats have to defend 24 seats, including seats in 10 states that Trump won in the 2016 presidential election.

There is only one Republican running for reelection in a state that voted for Democratic nominee Hillary Clinton Hillary Diane Rodham ClintonFox News poll: Biden ahead of Trump in Nevada, Pennsylvania and Ohio Trump, Biden court Black business owners in final election sprint The power of incumbency: How Trump is using the Oval Office to win reelection MORE, while five Democrats are running in states that Trump won by double digits: Indiana, Missouri, Montana, North Dakota and West Virginia.

Future Republican control of the House is more in doubt.

House Republicans need to defend 25 seats carried by Clinton in 2016, and Democrats need to flip only 23 to capture the majority.

Republicans want Ducey to appoint someone who will be a more reliable vote on health care in case they retain their congressional majorities.

“I want somebody who is for affordable health care, and right now ObamaCare is not affordable, nor is health care, which is a direct result of ObamaCare,” Cassidy said.

Ducey, who was governor when the Senate debated ObamaCare repeal legislation in 2017, initially had serious reservations about the GOP bill.

Arizona was a state that opted to expand Medicaid coverage under ObamaCare, which enabled almost 500,000 residents in the state to gain health coverage.

But in a phone call with McCain shortly before his dramatic “no” vote, Ducey recommended that the senator vote for it, McCain recalled in his book “The Restless Wave.”

“On balance he thought it was worth voting for,” McCain wrote.

A Republican senator who requested anonymity to discuss Ducey’s choice said he expects the governor will tap someone who is more aligned with his political views.

“I think he’s going to pick someone where he knows the answers to those questions,” the senator said.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump 'no longer angry' at Romney because of Supreme Court stance On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline The Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power MORE (R-Ky.) is keeping his agenda for next year secret.

He declined on Tuesday to say whether Republicans would make another push to repeal ObamaCare if they keep control of Congress.

“I’m concerned about September,” McConnell told reporters, emphasizing that he’s more focused on the remaining 2018 agenda. “We have, I hope, three conference reports on minibuses; I hope a conference report on the farm bill; I hope an up-or-down vote on a bipartisan opioid agreement.

“We have a full plate for September, and I’m not willing to speculate beyond the end of September,” he added.