Half of the 1,002 adults surveyed from Friday through Monday supported Bush's plan to strengthen border security while also establishing a guest worker program. One-third of respondents voiced opposition to the plan.
However, the poll found wide disparities among conservative voters - 44 percent were more hard-line, favoring full-out deportation of illegal immigrants, the Journal said.
Democratic pollster Peter Hart, who helped conduct the poll, said Bush appears to have won public support but not necessarily his party's.
"The difficulty is, the base of the Republican Party is marching in the other direction," Hart told the Journal.
The poll had a margin of error of 3.1 percentage points.