Senate majority leader Mitch McConnell on Thursday hinted that the Republican effort to repeal the Affordable Care Act (ACA) could fall short as conservatives and moderates in his conference remain at an impasse over key aspects of the bill.

Before leaving Washington for a week-long Fourth of July recess, McConnell delayed a vote on the Republican healthcare bill after it was clear there was not enough support for the plan, which would leave 22 million fewer people without health insurance over the next decade, according to an analysis by the Congressional Budget Office.

“If my side is unable to agree on an adequate replacement, then some kind of action with regard to the private health insurance market must occur,” McConnell told constituents at a Rotary Club lunch on Thursday, according to the Associated Press.

“No action is not an alternative,” he added. “We’ve got the insurance markets imploding all over the country, including in this state.”

McConnell’s comments were quickly embraced by his Democratic counterpart, Senate minority leader Chuck Schumer.

“It’s encouraging that Senator McConnell today acknowledged that the issues with the exchanges are fixable, and opened the door to bipartisan solutions to improve our healthcare system,” Schumer said in a statement.

“As we’ve said time and time again, Democrats are eager to work with Republicans to stabilize the markets and improve the law. At the top of the list should be ensuring cost-sharing payments are permanent, which will protect healthcare for millions.”

McConnell faces a daunting task as he works behind the scenes with senators to craft a bill that bridges the ideological divide within his conference. Moderates, especially those from states that opted to expand Medicaid under the ACA (also known as Obamacare) are wary of scaling back spending on the health insurance program for low-income Americans, and conservatives are irked the plan does not go further to repeal the law.

“I’m in the position of a guy with a Rubik’s cube – trying to twist the dial in such a way to get at least 50 members of my conference who can agree to a version of repealing and replacing Obamcare,” McConnell told Kentucky voters at a town hall-style event on Thursday, according to NBC. “That is a very timely subject that I’m grappling with as we speak.”

Senate minority leader Chuck Schumer holds up a photograph of constituents who would be adversely affected by the proposed Republican bill. Photograph: Andrew Harnik/AP

An initial draft of the Senate Republican healthcare plan mirrors the structure of the House bill, which passed in May. The measure would repeal key pieces of the ACA while extracting deep cuts to Medicaid compared to spending under current law.

McConnell has since made changes to the bill, including adding $45bn to combat the opioid epidemic, among other adjustments. The CBO is expected to release another analysis sometime next week, a likely indicator that Senate Republicans will not vote on the plan until later this month.

On Thursday, a handful of senate Republicans echoed McConnell’s skepticism about whether the party would be able to reach an agreement on healthcare.

“It is precarious,” senator Ted Cruz, a conservative of Texas, said on San Antonio’s KTSA Radio. “The majority is so narrow, I don’t know if we get it done or not.”

Senate Republicans are using a special budget process known as reconciliation to avoid a Democratic filibuster of the repeal plan. To pass the bill, Republicans need support from at least 50 of their 52 members. No Democrats are expected to support a repeal measure. In the case of a tie, vice-president Mike Pence would cast the final vote.

Cruz has offered an amendment that would allow insurance companies to sell non-compliant plans as long as they also offer at least one plan that does meet Obamacare standards. Experts on both sides of the political debate said such an action could devastate insurance markets.

Senator Jerry Moran, a Republican from Kansas who surprised his party when he came out against the bill, told constituents in Palco that healthcare reform is “almost impossible to try to solve when you’re trying to do it with 51 votes in the United States Senate, in which there is not significant consensus on what the final result ought to be”.

As the debate over healthcare rages, Senator Pat Toomey, a Republican of Pennsylvania who supports the bill, suggested during a televised town hall on Wednesday that McConnell was “several weeks away” from winning enough support for a vote. Asked why Republicans were struggling to fulfill a years-long campaign promise, Toomey offered a candid reply.

“Look, I didn’t expect Donald Trump to win,” he said. “I think most of my colleagues didn’t, so we didn’t expect to be in this situation.”