If Democrat Alex Sink had prevailed in Tuesday’s special election in Florida, Democrats would have said many things. They would have asserted that her victory showed that Obamacare was not the powerful issue Republicans thought it was. They would have noted a Democrat’s ability to pick up a formerly Republican House seat in a district that President Obama had carried in 2012 by just 50-to-49 percent. This, they would have insisted, was a good sign for this fall’s midterms.

The problem for Democrats is that Sink lost to Republican David Jolly by just over 3,400 votes. Republicans immediately offered the mirror image of the Democrats’ talking points. House Speaker John Boehner sent out a tweet that ended: “#ObamaCare disaster.” He reiterated his message in another tweet a few minutes later:

Many Republicans argued that if the Democrats could not win this district, they were going have a lot of trouble picking up seats anywhere else.

There are always caveats about making too much of special elections. There is a large difference between Tuesday’s turnout in Florida’s 13th District and normal turnout. About 182,000 voters cast ballots on Tuesday, compared with nearly 330,000 in 2012 and 267,000 in the last mid-term elections. Lower turnouts favor Republicans.

But Democrats should not fool themselves about this result. It is a huge disappointment for them, and an important Republican victory. It is a sign that Democrats need to retool their response on Obamacare and sharpen their economic arguments. In a race that cost some $12.7 million, outside conservative groups ran an aggressive and coordinated campaign to discredit Obamacare and Sink. This sort of thing will happen for the rest of the year in district after district, and state after state. If Democrats aren’t effective in discrediting the outside groups and their misleading ads against the health-care law, they will confront more results like Tuesday’s.

Sink did a decent job mobilizing early voters and narrowly carried them. But Jolly won by even more among voters who cast ballots on Election Day itself. This just underscores a truth that everyone is aware of: Voter turnout efforts will be central to how the rest of the 2014 races turn out.

On Tuesday morning, before the results were in, Greg Sargent made a good case on his Plum Line blog against making too much of the Florida 13 result one way or another. He argued that it’s a mistake to judge what the impact of Obamacare in November — eight months from now – on the basis of a single special election in March. I agree with that, and Republicans may well be taking the wrong lesson if they put too much of their money on the-health care issue this fall. A lot depends, as Sargent argued, on “how the law fares over time.”

Nonetheless, this was a rare toss-up seat that Democrats should have been able to win. Republicans and their outside allies will be encouraged to spend more, and they will have an easier time raising the money. No wonder John Boehner was tweeting so much.

E.J. Dionne writes about politics in a twice-weekly column and on the PostPartisan blog. He is also a senior fellow in Governance Studies at the Brookings Institution, a government professor at Georgetown University and a frequent commentator on politics for National Public Radio, ABC’s “This Week” and NBC’s “Meet the Press.”