That's the finding of a Gallup poll released Friday. While 41 percent of respondents favor cutting immigration, one-third say the current number of legal immigrants is the right one.
In 1999, 10 percent of those polled wanted to increase immigration.
College graduates and people with post-graduate education are more likely to favor higher levels of immigration, with 30 percent of both groups saying the United States needs more immigrants. Only 19 percent of those with some college or with a high school diploma or less agreed.
Gallup suggested that reflects the debate on increasing the number of highly skilled and educated immigrants to work in high-tech jobs.
Republicans are less likely than Democrats and independents to support higher levels of immigration, with 50 percent saying fewer people should be legally admitted to the United States. House Majority Leader Eric Cantor, R-Va., lost to a primary challenger earlier this month at least partly because he was painted as being soft on immigration.
While wanting more immigrants admitted is a minority view, a majority say immigration is good for the United States. That dropped from 72 percent in 2013 to 63 percent this year.
The issue is a volatile one, with fewer than 60 percent describing immigration as good immediately after the 2001 terrorist attacks and during the worst of the 2009 recession.
Gallup polled 1,027 adults by telephone between June 5 and June 8. The margin of error is 4 percentage points.