A Pennsylvania special election scheduled for May 18 may provide an early glimpse for anyone wondering how big a millstone the health care law will be for Democrats this fall.

The state’s 12th Congressional District, which meanders through rural southwestern Pennsylvania, skirting the suburbs of Pittsburgh and including the blue-collar cities of Latrobe and Johnstown, was represented by Democratic Rep. John Murtha for 36 years, until his death in February. Now Murtha’s top aide, Mark Critz, hopes to succeed his former boss. He is, however, running into an unexpectedly strong challenge from Republican Tim Burns, who has made repeal of the health law central to his campaign.

Going by numbers, Mr. Critz should be the likely winner. Although Sen. John McCain carried the district by a small margin in 2008, Democrats outnumber Republicans 2–1, and the district has a high concentration of union workers. Sen. John Kerry won the district in 2004, and Al Gore carried it in 2000.

Mr. Burns, a political newcomer, has countered this Democratic advantage by hammering the health care law. In fact, while the district has been hard hit by the recession and economic issues clearly will be important, Mr. Burns says he has found the health care law to be “the dominant issue on voters’ minds.”

Both Mr. Burns and the National Republican Congressional Committee have been bombarding the district with television and radio ads attacking the law, warning that it will raise taxes, cost jobs and cut Medicare. (The latter seems just a touch unfair. The cuts are real, of course, but given Medicare’s enormous future shortfalls, such cuts are inevitable regardless of which party is in power.)

“Americans said ‘no’ to government-run health care, but Congress and liberals like Mark Critz didn’t listen,” one 30-second ad says, adding that Democrats “rammed through” a piece of legislation that “Pennsylvanians didn’t want and can’t afford.”

Mr. Burns’ message would appear to have a receptive audience. A recent Rasmussen poll showed that 53 percent of Pennsylvanians thought the health care law was bad for the country, while just 36 percent supported it. Fully 60 percent of Pennsylvania voters want to repeal the law; 47 percent of voters “strongly favor” repeal.

In response, Mr. Critz has tried to back away from the law, but without angering his union and Democratic establishment backers. Before the law passed, he declined to say how he would vote on it. Now, he opposes repeal but says he wants to go to Washington to “fix” the law. He worries that the law might have been too expensive but calls for changes that actually would increase its cost. In one recent statement, he phrased it this way: “We need health insurance reform but it must be done in a way that is consistent with our values.” That clears it up.

The most recent poll by the Pittsburgh Post-Gazette gives Mr. Burns a narrow four-point lead, with 13 percent of voters still undecided. That leaves the race very much up in the air. Many district voters retain warm memories of Mr. Critz’s former boss, Murtha. He also may benefit from a union get-out-the-vote effort and a hotly contested Democratic primary for U.S. Senate on the same day.

However, if Mr. Burns is able to ride opposition to the health care law to victory, it will serve as a template for Republicans nationwide. Democratic pollsters Patrick H. Caddell and Douglas E. Schoen already are calling the health care vote “an incontrovertible disaster” for their party. Republican candidates from New York to California are making “repeal” part of their platforms. A Burns victory would further energize that effort.

In fact, if Mr. Burns wins this May, it won’t just be bad news for Democrats looking to November. It will be another sign that President Obama’s health care victory may be fleeting.