Democrats say the current law is a solid basis for what could be a much better health care system. However, the status quo is insufficient, they argue, and must be supplemented with additional reforms, some of which Republicans and the insurance industry abhor.

Related: Obama administration seeks dismissal of insurer ACA lawsuits

President Obama recently outlined a number of changes he hopes Congress will work with his successor to implement.

One of his chief priorities is to convince the 19 states that have continued to resist the expansion of Medicaid to reverse course, likely by offering them several years of the expansion paid for entirely by the federal government, as was the case for the states that embraced the expansion in 2014. That plan will likely face resistance from Congressional Republicans, however.

Other changes that Democrats say will help save the law involve preserving funding to help insurers who have endured losses in the first years of the ACA weather the tough times as well as payments to insurers that the administration has made that allow the insurers to offer low-cost plans to certain customers. Republicans in Congress have sued over the latter program, saying the administration did not have the authorization to make those payments without Congressional approval.

Democrats have also called for even greater tax credits to help people afford ACA plans.

Finally, Obama, who has largely avoided talk of a "public option" since the idea was scrapped during the crafting of the ACA in 2009, is now calling for a government-run insurance plan to be sold in addition to the private plans available currently through Healthcare.gov.

The public option, which Hillary Clinton also endorsed after dodging questions about it throughout much of her primary campaign against Bernie Sanders, is unlikely to materialize unless Democrats are able to win big majorities in both the House and the Senate.

One area of agreement between Republicans and Democrats is that the ACA marketplace needs to implement stricter rules to ensure that customers are not signing up for insurance plans only after they get sick. Legislation authored by Republicans in the House would include sharp limits on who can use "special enrollment periods" to enroll in ACA plans outside of the typical open enrollment period.

Some conservatives have called for allowing insurers to charge much greater premiums for ACA plans based on age. Currently insurers can charge older customers a maximum of three times more than younger customers for the same health plan.