Rasmussen Reports said the 61 percent who agree is the highest figure on the question in five years. Fewer than three out of 10, 28 percent, support birthright citizenship for everyone, down 6 percentage points since August.
The Constitution was amended after the Civil War to guarantee citizenship to anyone born on U.S. soil, independent of their parents' status. That means a change would require another constitutional amendment.
Republicans, at 77 percent, and independents, at 63 percent, are more likely to oppose birthright citizenship than Democrats, who are evenly divided on the issue.
The poll found overwhelming support for requiring anyone seeking federal or state benefits to prove citizenship, with 84 percent agreeing.
A majority of those surveyed said the federal government encourages illegal immigration. They were split on whether states should adopt their own immigration policies.
Rasmussen surveyed 1,000 likely voters April 17 and April 18. The margin of error is 3 points.