WASHINGTON  A bare majority of Americans support President Obama’s plan to send 30,000 more troops to Afghanistan, but many are skeptical that the United States can count on Afghanistan as a partner in the fight or that the escalation would reduce the chances of a domestic terrorist attack, according to the latest New York Times/CBS News poll.

In the wake of the president’s address last week explaining his decision, the poll found a 10 percentage point increase in public approval of Mr. Obama’s handling of the war in Afghanistan since last month, to 48 percent. But the shift reflects a twist on the political polarization that has marked much of Mr. Obama’s first year in office: Republican and independent voters are rallying behind Mr. Obama as he presses for the troop escalation, while Democrats remain decidedly cool to his war plans.

The poll showed a steady slide in support for Mr. Obama as he approaches the end of his first year in office. His job approval rating has now hit 50 percent, the lowest yet in this poll; it was 68 percent at its peak in April. The percentage of Americans who approve of his handling of the economy has dropped to 47 percent from 54 percent in October. And 42 percent approve of the way he is handling health care, down five percentage points in the last few months.

Mr. Obama has spent much of the past three months trying to rally support for a health care bill and formulating a plan for Afghanistan. But in the poll, 12 percent of respondents said health care was the biggest problem facing the nation, while just 2 percent named Afghanistan. Nearly 50 percent listed the economy or jobs.