Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeRepublican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style Bush endorsing Biden? Don't hold your breath MORE (R-Ariz.) cast doubt on the GOP's hopes of voting by August on a measure repealing and replacing ObamaCare, warning business leaders in Arizona this week that Republicans might not be successful in their efforts to overhaul healthcare.

“There are some still saying that we’ll vote before the August break," he said at members of the Chamber of Commerce in Glendale, Ariz., according to The Washington Post. "I have a hard time believing that."

While the House passed its version of a healthcare reform bill — the American Health Care Act — last month, Senate Republicans are working on their own healthcare legislation.

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GOP congressional leaders have voiced optimism on the timeline for passing the Senate bill, however, setting their sights on a vote by August. Senate Majority Whip John Cornyn John CornynBipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection Airline job cuts loom in battleground states MORE (R-Texas) was even more optimistic, saying on Wednesday that healthcare will be "done by the end of July at the latest."

"We do need to take care of our business, and I think you mentioned healthcare, and that's certainly front and center in the United States Senate — something we're going to have to get resolved here in the next few weeks," Cornyn told radio host Chad Hasty. "I don't think we have any choice."

Repealing and replacing ObamaCare would fulfill a longtime campaign pledge by Republicans. But the GOP lawmakers have also faced backlash from some constituents in recent months amid concerns that their healthcare reform efforts could result in higher insurance premiums for low-income Americans and an end to the Affordable Care Act's protections for consumers with pre-existing conditions.