As lawmakers return to Washington after the week-long Fourth of July recess, top Senate Democrats are urging Senate Majority Leader Mitch McConnell to work across the aisle to stabilize Obamacare's markets.

Senate Minority Leader Chuck Schumer, D-N.Y.; Democratic Whip Dick Durbin, D-Ill.; Health, Education, Labor and Pensions Committee ranking member Patty Murray, D-Wash.; and Democratic Policy and Communications Committee Chairwoman Debbie Stabenow, D-Mich.; sent a letter to McConnell on Monday outlining reforms they believe would "provide stability and certainty" to the health insurance markets.

"We believe it is important for the Senate to focus on common sense reforms to make the healthcare system more affordable and workable for American families, including guaranteeing cost-sharing reduction payments, creating a permanent reinsurance program, addressing areas of the country without insurers, and easing the current cliff on cost-sharing subsidies," the senators wrote. "Such reforms would have an immediate effect on stabilizing the market while lowering premiums."

In their letter, the senators pointed specifically to four different bills that would address these issues, and said Democrats are willing to work with Republicans to implement reforms.

"We stand ready to work on these and other reforms to the current system and urge you to join us in advancing measures that would have an immediate impact on improving the health care system for American families," they wrote.

The Senate Democrats were responding to comments made by McConnell, R-Ky., last week at a Rotary Club meeting in Kentucky, during which he conceded Republicans may have to work with Democrats if they can't pass their own replacement plan.

"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 said, according to the Associated Press. "No action is not an alternative. We've got the insurance markets imploding all over the country, including in this state."

McConnell's comments were a departure from prior statements on Obamacare. During his 2014 re-election campaign, the Kentucky Republican pledged to repeal Obamacare "root and branch."

But the GOP has struggled to gain consensus around a plan to repeal and replace the 2010 healthcare law.

After the House passed its healthcare proposal in May, Senate Republicans put forth their own plan last month. But the bill was criticized by conservative and moderate senators alike, though for different reasons.

As opposition to the legislation grew, McConnell delayed a vote on the plan and vowed to continue working on the bill when Republicans returned to their districts last week.

But some Republicans, including the majority leader, are now raising the possibility of working across the aisle to stabilize the market if consensus can't be reached.