Fifty-one percent of respondents in the CNN poll said they support a bill that would attempt to increase border security and create a pathway to citizenship, CNN said, while 45 percent were opposed to the measure.
"Support comes mostly from Democrats -- six in 10 favor the bill -- with independents and Republicans split right down the middle," CNN Polling Director Keating Holland said. "There is also a generation gap on this issue, with senior citizens opposed to the bill by a 17-point margin while younger Americans tend to favor it."
Sixty-two percent of respondents said border security should be the bill's main focus while 36 percent said that a path to citizenship should be the priority.
The poll's release comes as some Republican senators are preparing an amendment to the immigration bill that they say would bolster border security, CNN said.
ORC International conducted the poll for CNN June 11-13, with 1,1014 adults nationwide questioned by telephone.
The sampling error is 3 percentage points.