The law, signed by Republican Gov. Greg Abbott, bans abortions after about six weeks of pregnancy, which is before many women know they're pregnant. It also allows private citizens to sue abortion providers or anyone who helps a woman obtain an abortion.
The survey found that almost 6 in 10 Americans oppose a ban on abortions after cardiac activity is detected, at about six to eight weeks into a typical pregnancy.
That includes 59% of Republicans, 61% of Democrats and 53% of independents.
The poll of 1,220 adults was conducted from Sept. 20 to 26 and has a margin of error of 3.4 percentage points, meaning results could be about 3 points higher or lower.
White college graduates are most against this provision, including 71% of white women with college degrees and 64% of white, college-educated men.
But even whites without college degrees, a group that leans heavily toward Republicans, are also opposed, including 61% of non-college-educated women and 56% of white men without degrees.
Latinos, a group that skews Catholic, are the most supportive of this kind of law at 44%, but 46% of Latinos are also opposed.
When it comes to whether private citizens should be allowed to sue abortion providers or anyone who assists a woman in getting an abortion, this is wildly unpopular.
Three-quarters of respondents said they are against this, including 57% of Republicans, three-quarters of independents and 9 in 10 Democrats.
Again, white college graduates are the most opposed to this — 80% — but two-thirds of whites without college degrees feel the same way.
Even white evangelical Christians are largely against it — 57% — as are a slim majority of Trump supporters — 52%.