WASHINGTON (CNN) -- It's one of the hottest and most controversial issues in front of lawmakers this summer.
And as both federal and state legislators grapple with increased restrictions on abortion, a new national poll indicates Americans have mixed reactions to some of the moves being made right now in state houses and the nation's capital.
According to an ABC News/Washington Post poll released Thursday morning, a majority of the public favor banning most abortions after 20 weeks into a pregnancy, but a majority oppose moves by some states to impose new restrictions and regulations on abortion providers.
Fifty-six percent of those questioned in the survey say that they support the 20-week ban, with 27% saying they prefer preventing most abortions after 24 weeks of pregnancy, as the Supreme Court ruled in the landmark Roe v. Wade case.
Forty-eight percent of Americans questioned in a United Technologies/National Journal poll conducted late last month said they supported a bill that would ban most abortions after 20 weeks, with 44% opposed.
Last week Texas Gov. Rick Perry signed into law a 20-week ban. A number of states have passed such restrictions in recent years, including Nebraska, Kansas, Louisiana, Oklahoma, Indiana and Alabama. Arkansas has a ban for pregnancies beyond 12 weeks, but a pending court challenge is preventing the ban from going into place.
North Dakota has the tightest restriction in the country at six weeks, when a fetal heartbeat can be detected. But earlier this week a federal judge put a temporary hold on the implementation of the law.
On the federal level, the GOP-controlled House recently passed a similar late-term abortion ban bill, with only six Republicans voting against the measure and only six Democrats voting in support of it. The bill prohibits most abortions for women beyond their 20th week of pregnancy.
While the original House measure included an exception for cases in which the health of the mother is in danger, Republicans got strong pushback for not including exceptions for pregnancies that resulted from rape or incest. Republican leaders later added new language to include those exceptions.
Senate Republicans are considering sponsoring a similar bill. Sen. Marco Rubio, a possible 2016 contender for the GOP nomination, may take the lead in introducing the measure.
"If someone else would like to do it instead of me, I'm more than happy to consider it. But I'd like to be the lead sponsor," the Florida Republican said in a Politico report, which Rubio's office confirmed to CNN. "I feel very strongly about this issue. And I'd like to be the lead sponsor on it if we can find language that we can unify people behind."
Such a bill would face major opposition in the Democratic controlled chamber, but Senate Majority Leader Harry Reid said earlier this month that he would be open to allowing such a bill to be introduced.
Republican governors in Ohio and Wisconsin recently signed into law increased abortion restrictions, and North Carolina lawmakers are close to passing a similar measure.
According to the poll, 54% say they oppose state laws that make it increasingly more challenging for abortion clinics to operate, with 45% saying they support such moves.
The survey indicates that overall, 55% say that abortion should be legal in all or most cases.
The ABC News/Washington Post poll was conducted July 18-21, with 1,002 adults nationwide questioned by telephone. The survey's overall sampling error is plus or minus three percentage points.
CNN's Ashley Killough contributed to this report.