People argue that Romney implemented an Obamacare-like medical system in his own state. If it was possible without federal involvement why wouldn't Democrats follow the example with the most populous Democratic states like California and New York?
In order to implement Romneycare in Massachusetts, Mitt Romney had to get waivers from the federal government. In particular, Romneycare made changes to how Medicaid money was spent. Since both Romney and George W. Bush were Republicans, it was easier for Romney to get that kind of approval than it would have been for a Democrat.
You might ask why they couldn't have implemented Obamacare on a state by state basis in 2009 and 2010, when the Democrats controlled the presidency and Congress.
They didn't want to do so. Democrats believe in national solutions. When they had the power to do a state by state solution, they had the power to do the national solution. So that's what they did, the national system that they preferred.
Healthcare is expensive. The highest state income tax now is 13.3% (top rate in California). The top federal income tax rate was 36% or 38.3% with Medicare (adjusting basis 38.9/101.45%). Which tax bill could more easily hide (or absorb) additional tax increases?
States could compete. Democrats couldn't have passed state versions of Obamacare in every state. So California might have passed it, and increased their tax bill sharply. Meanwhile, Texas does not pass it. People (and/or businesses that employ people) move from states that did pass it (e.g. California) to states that did not.
Federal budget gimmicks. Obamacare used two budget gimmicks that only work in the federal budget.
Medicare. Obamacare took a bunch of bipartisan recommendations on saving money in Medicare and used them to make its budget numbers look better. These savings had been intended to pass something called the doc fix, but Obamacare hijacked them for its own purposes. The really gimmicky part of this is that they didn't reduce long term spending on Medicare. The savings were left in the Medicare trust fund so they can still be spent in the future. But by not spending them now, they make the short term budget deficit look better.
Student loans. Democrats nationalized the subsidized student loan program as part of the Obamacare bill. In theory, this reduces costs, as this reduces the subsidies. This had nothing to do with healthcare but was deficit negative on the scoring, so they included it in Obamacare.
States couldn't use either of those gimmicks in their own programs, as Medicare is a purely federal program and student loan subsidies were federal (albeit state administered). So states couldn't change Medicare at all and could only change students loans with federal support.
You might ask why they don't do that now.
They don't want to do so. They'd prefer the current system for the same reasons they preferred it previously.
Obamacare still exists. Until it is actually repealed, there is no reason to replace it at the state level. In fact, they can't, as Obamacare preempts state action (as it preempted Romneycare in Massachusetts). Beyond that, they don't even know what changes might be made at the federal level. Until repeal is completed, the states have no idea what they need to do.
They can't in most states. Republicans control the executive and legislative branches in a majority of the states (twenty-six out of fifty). Democrats only control six states. The remainder are shared. So Democrats might possibly replace the federal Obamacare in six states. In other states, they'd have to work with Republicans if they wanted to do something like that.
This may change as elections progress. For example, if Democrats win the governor's race in New Jersey in 2017 and hold their current legislative seats, that would be a seventh state. But most states don't have their elections until 2018, so it would be 2019 before changes could be made by elections (resignations, retirements, and tragedies might cause earlier changes but usually don't).
Another issue is that in really Democratic states, what they'd really like to do is single payer. Single payer is even more expensive and difficult to coordinate with the federal government (the federal government spends directly on healthcare through both Medicare and Veterans' Affairs). Vermont considered and then abandoned a single payer program due to the expense.
Not a very in-depth article, but this article talks about some of the proposals that have been floating around at a state level and summarizes with this:
Nationally, Medicaid coverage has one of the highest satisfaction rates among consumers...Supporters of single-payer health care often point to those satisfaction rates as proof that a government-run health plan would be preferable to the current system...
...plenty of challenges remain. Funding is always an issue, and rising taxes is a turnoff to many consumers. Other consumers disagree with the premise that a government-run system would be an improvement on a privately-based one.
So it's politics. It's going to take time to politicians to make their case and assuage concerns of costs and general apathy towards government.
The article finishes with:
But despite the challenges, it could take just one success story. If one state is able to develop a working universal health care plan, consumers across the country could warm up to the idea.
This is how it worked in Canada. Saskatchewan created a government run system in 1947. Alberta followed in 1950 and that led to the eventual adoption nationally.
In the US a (semi related) comparison could be made to marijuana legalization...a concept frowned upon nationally for many decades, but once one state decided to legalize (CO), then the rate of other states legalizing it quickly increased.