(CNN) American political parties are running to the extremes on abortion as conservative lawmakers vie to impose stricter limits on terminating pregnancies, prompting Democrats to rally in defense of women's reproductive rights -- and the landmark 1973 Roe v. Wade decision.

But the country remains planted somewhere in the middle. The public largely thinks that abortion should be legal, but is extremely divided on how.

That's how it comes to be that a Republican governor in Vermont is allowing an abortion rights bill to become law and a Democratic governor is set to sign one curbing abortion rights in Louisiana.

Public support for Roe

Nearly half of Americans (48%) say they would be dissatisfied or angry if the ruling were overturned, 23% say it wouldn't matter much and 26% would be happy or satisfied. Although there isn't much of a gender gap on whether the court should maintain Roe (69% of women and 65% of men say so), women are more apt to say they would be angry if it were overturned (38% vs. 24% among men).

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The poll also finds that 44% of Americans think abortion should be generally available, 34% that it should be available but under stricter limits than it is now and 20% that shouldn't be permitted at all.

About half of Republicans in the CBS poll (48%) think the Supreme Court should keep Roe. Democrats are more aligned. The vast majority (87%) would keep it and only 11% of them think the Supreme Court should overturn it.

Quinnipiac University poll also conducted in May finds 60% of voters think abortion should be legal in all or most cases, while 35% said it should be illegal in all or most cases. When asked specifically whether it should be legal in instances of rape or incest, 82% say it should be. But while 41% say they support "banning abortion after a fetal heartbeat is detectable, which is usually around six weeks of pregnancy," 48% say they oppose such a law, including 51% of women. Almost 6 in 10 in that poll, 57%, say they think it's unlikely that Roe v. Wade will be overturned within the next few years, while 29% believe that is likely.

A top issue for Democratic candidates

It's clear that 2020 is going to be an election largely built around a national divide on the issue and the coming Supreme Court fight, particularly among Democrats as they seek to mobilize female voters against Trump and Republicans try to keep conservatives fired up.

That's why a pack of Democratic presidential candidates joined demonstrations in front of the Supreme Court on Tuesday.

Sens. Kirsten Gillibrand of New York and Elizabeth Warren of Massachusetts would codify Roe v. Wade into law

Abortion rights activists rally outside the U.S. Supreme Court on May 21, 2019.

They've both also proposed ending the Hyde Amendment, language included in US spending bills since 1994 that bans the use of taxpayer funds for abortion except in cases of rape and incest. So have Sen. Cory Booker of New Jersey, former Rep. Beto O'Rourke of Texas and South Bend, Indiana, Mayor Pete Buttigieg.

O'Rourke was not at the Supreme Court but rather at a CNN town hall Wednesday night, where he also made a pledge about Supreme Court justices.

"As president, I will make sure that every nominee to every federal bench, including the Supreme Court, understands and believes that the 1973 decision, Roe v. Wade, is the settled law of the land," O'Rourke said.

That could be a meaningless test, however, because Republican nominees to the court have also said they would respect the precedent of Roe, although it is the appointment of conservative Justice Brett Kavanaugh that made overturning Roe seem possible.

"As a judge, it is an important precedent of the Supreme Court," Kavanaugh said during his confirmation hearing. "I said that it's settled as a precedent of the Supreme Court."

We'll see how that works out, whether conservatives who were counting on Kavanaugh to undermine Roe get their way -- or the Republicans who support abortion rights, like Sen. Susan Collins of Maine, who supported his nomination in part because she was convinced he would not vote to overturn it

Abortion can scramble party lines

In Vermont, the Republican governor, Phil Scott, describes himself as "pro-choice" and will allow a bill to become law that will, according to CNN's report, "recognize as a fundamental right the freedom of reproductive choice" and "prohibit public entities from interfering with or restricting the right of an individual to terminate the individual's pregnancy." The measure would also protect "rights to choose or refuse contraception or sterilization or to choose to carry a pregnancy to term, to give birth to a child, or to obtain an abortion."

Collins and Scott are Northeastern Republicans who support abortion rights. There are Democrats in the South who do not.

A Louisiana bill that would outlaw abortions after six weeks of pregnancy -- it is among a raft of bills that states have passed in recent months -- was introduced by a Democrat, state Sen. John Milkovich, and it is a Democratic governor, John Bel Edwards, who has said he would sign it.

A much more restrictive law that passed in Alabama drew criticism from Republicans with strong anti-abortion-rights records, like Mitt Romney, and those newer to the issue, like Trump

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And some politicians, of course, try to have it all ways. The Democratic front-runner in the 2020 presidential primary race, former Vice President Joe Biden, had a long career as a dealmaker in the Senate, where he supported the Hyde Amendment. But this week Biden endorsed repealing the amendment, according to reports

Biden, who is Catholic, has long said he personally opposes abortion, but has supported abortion rights.

"I accept my Church's position on abortion as a what we call de fide doctrine. Life begins at conception. That's the Church's judgment. I accept it in my personal life," he said. "But I refuse to impose it on equally devout Christians and Muslims and Jews. I just refuse to impose that on others," he said.

He added: "I do not believe that we have a right to tell other people, women, that they can't control their bodies. That's a decision between them and their doctor, in my view, and the Supreme Court, I'm not going to interfere with that."