The New York Times/CBS News poll found that 54 percent of Americans say they think gun-control laws should be tightened, up markedly from a CBS News poll in April that found that only 39 percent backed stricter laws.
A gunman killed 20 children, six adults and himself at the school Dec. 14.
The poll also found that most of 1,110 respondents -- about 90 percent -- said they would support a background-check requirement for all gun purchases, and about 60 percent of respondents said they would support a ban on high-capacity magazines, such as the 15- and 30-round magazines that have been used in several recent mass shootings.
"I'm from a rural area in the South, I grew up in a gun culture, my father hunted," Leslie Hodges, a 64-year-old gun owner from Atlanta, said in a follow-up interview. "However, I don't believe being able to have a gun keeps you from thinking reasonably about changes that would keep someone from walking into a school and being able to kill 20 children in 20 seconds. I think that we can say, O.K., we want the freedom to have guns in this country, but there are rules we can all agree to that will make us all safer."
The national poll was conducted Jan. 11 to Jan. 15, before the president announced his proposals to curb gun violence. It has a sampling error of plus or minus three percentage points.
Another poll, an NBC News/Wall Street Journal survey, showed that the National Rifle Association is more popular than Hollywood.
The powerful lobby for gun makers and gun owners has a 41 percent positive approval rating, while Hollywood and the entertainment industry have a 23 percent favorable rating, the poll found.
The NRA and other critics have blamed the entertainment and video-game industries for contributing to an American culture of violence.
The poll found 34 percent of respondents gave the giant gun-rights group a negative rating, while 46 percent said the same about Hollywood and the entertainment industry.
At the same time, 56 percent of Americans said laws covering the sale of firearms should be made stricter, the poll found.
Views about guns were closely tied to whether the respondent households had a gun, the poll found. Sixty-seven percent of people in homes without guns favored stricter laws while 44 percent in homes with guns favored making them stricter.
The NBC News/Wall Street Journal poll found 41 percent of Americans said someone in their household owned a gun.
The poll of 1,000 adults was conducted Jan. 12-15 and has a margin of error of plus or minus 3.1 percentage points.