President Barack 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 with the public, according to the latest New York Times/CBS News poll.

As he prepares to deliver his final State of the Union address on Tuesday, 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 Obama exceeded his authority with his executive actions on gun control as said he acted properly.

Overall, 46 percent of Americans approve of his handling of the job, while 47 percent disapprove, placing him below Ronald Reagan and Bill Clinton at this stage of their presidencies, but significantly above George W. Bush. Democrats remain broadly supportive of the president, and about 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, Sen. Bernie Sanders of Vermont and former Gov. 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 with the general public in the fall.

Of the issues tested, Obama is at his weakest on foreign policy, with just 34 percent approving of his performance. Only 37 percent approve his immigration policies and 40 percent of 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 plans to spend much of his speech on Tuesday night highlighting the recovery of the economy on his watch. His Republican opponents, zeroing in on his weak areas, have focused in recent days on what they see as his foreign policy failures in places like 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. That has not changed drastically with the arrival of new management. Public opinion of Congress is still stubbornly low, with just 15 percent approving and 75 percent disapproving.

The new House speaker, Paul D. Ryan, has a challenge consolidating support among Republicans, who split with 34 percent approving of his performance, compared with 23 percent disapproving. Ryan took over from Speaker John A. Boehner after a conservative revolt, but some on the right remain suspicious of their new leader despite his conservative record.

The latest poll was conducted after Obama announced his 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. As with other issues, that one broke down along party lines, with three-quarters of Democrats concluding that he acted within bounds and a roughly equal proportion of Republicans disagreeing.

While nearly 3 in 5 Americans would like to see stricter gun laws enacted, and 54 percent think such laws would help prevent gun violence, there is ground for consensus on the issue. Americans of all stripes with near unanimity support background checks for all potential gun buyers and strong majorities regardless of party affiliation think better mental health screening and treatment would reduce gun violence.

The nationwide poll was conducted from Jan. 7 to 10 with 1,276 adults on mobile telephones and landlines. The margin of sampling error is plus or minus 3 percentage points for all adults and 6 points for Democratic primary voters.