Last week I conducted a poll in the immediate aftermath of the Supreme Court’s ruling on Obamacare. By a margin of 50-45 percent, voters said they were displeased with the decision. They also said they disapproved of Obama’s handling of health care by 58-37. And, by counts of 56-21 and 52-21, they thought that both their health-care costs and their taxes would go up as a result of the court’s ruling.

But beyond the health-care decision, our poll also pointed to potential trouble spots for both parties in the weeks and months to come. For Obama, the challenges begin with domestic policy. Voters say that Romney would do a better job than Obama on most domestic issues—the economy (52 percent to 37 percent), illegal immigration (41-38), balancing the budget (48-44), fighting crime (35-33), holding the line on taxes (45-42), and health care (48-40). In addition, Obama's job-approval rating (45 percent) is well below the crucial 50-percent mark, and a plurality of voters (48 percent) say it is time to replace him with someone else, while only 42 percent say he has done his job well enough to deserve reelection.

That said, Republicans are facing trouble spots of their own. Overall, according to the poll, Romney trails Obama 44-47. He also trails Obama when it comes to who voters think would do a better job of handling education (40-48), foreign affairs (41-47), job creation (39-40), and terrorism (36-45). And 37 percent of voters say they trust the Democrats to do a better job of coping with the major issues the nation faces over the next few years, while 32 percent trust the Republicans. (One-quarter—24 percent—say they trust neither party.)

Meanwhile, voters are evenly split (42-42) over whether Obama or Romney would do a better job of reducing government spending. Given these numbers, it seems that if Republicans want to capitalize on voter anxiety about Obamacare increasing their taxes, they will have to do more than they currently are to emphasize their lower-tax message. The bottom line is that unless Romney and the Republicans are able to become credible advocates for comprehensive health-care policy in the context of cost containment and tax reform, they will not succeed politically.

Editor's note: Results inadvertently posted prematurely were removed on July 3, 2012.