NEW YORK —President Obama’s plan to expand background checks to cover more gun sales generated wide support among Americans, but it did little to improve his overall standing, according to a New York Times/CBS News poll.

Obama faces deep skepticism about his performance on a range of issues, including immigration, terrorism, health care, and gun policy. Moreover, nearly as many Americans said he exceeded his authority with executive actions on gun control as said he acted properly.

Overall, 46 percent approved of his handling of the job, while 47 percent disapproved, placing him below Ronald Reagan and Bill Clinton at this stage of their presidencies but significantly above George W. Bush. Democrats remain broadly supportive, and 3 in 5 potential Democratic primary voters said they wanted their nominee to continue his policies if elected.

The numbers suggested the challenge for former Secretary of State Hillary Clinton, Senator Bernie Sanders of Vermont and former governor Martin O’Malley of Maryland as they jockey for the party mantle. To win the favor of Democrats, they may not be able to veer too far from Obama, yet he remains weak enough that being seen as the embodiment of a third term might not help.

Obama polled weakest on foreign policy, with just 34 percent approving of his performance. Only 37 percent approved his immigration policies, and 40 percent his handling of terrorism.

His strongest area is the economy, and even there his ratings are mediocre, with 45 percent favoring his handling of the issue, compared with 49 percent disapproving.

On the heels of strong job-creation numbers, Obama planned to spend much of his State of the Union speech on Tuesday night highlighting the recovery of the economy on his watch. His Republican opponents have focused in recent days on what they see as foreign policy failures in Iran, North Korea, Syria, and Ukraine.

Obama, who has not enjoyed the support of a majority of Americans in the Times/CBS News survey since shortly after his second inauguration, in 2013, retains one saving grace, namely that Congress remains even less popular than he is. Public opinion of Congress is low, with just 15 percent approving and 75 percent disapproving.

The poll was conducted after Obama announced plans to expand the range of gun sellers who must conduct criminal background checks on customers and tighten enforcement of existing laws. More than 6 in 10 Americans support that, but they are divided on party and other lines. While 54 percent of Americans in households with a gun owner supported the action, 61 percent of those with a member of the National Rifle Association at home opposed it.

Overall, 49 percent of the public said Obama had acted within his authority, while 43 percent said he went beyond his power to regulate guns.

The Jan. 7-10 poll was of 1,276 adults on mobile phones and landlines. The margin of error is plus or minus 3 points for all adults and 6 points for Democratic primary voters.