Since the Supreme Court’s landmark Roe v. Wade decision in 1973, access to abortion has been one of the most contentious topics in American politics. The battle has raged across the country for the last four decades, as anti-abortion and abortion-rights activists have clashed in the courts, state houses, and the halls of Congress.

Last week's referendum in Albuquerque, where voters rejected a ban on abortion after 20 weeks, underscored a new development in the fight. And it also highlighted a fundamental disconnect in the way Americans approach restrictions on terminating pregnancies — particularly when they're asked to pull the trigger on a significant change to abortion law.

If it had passed, the measure would have been the first in the country to curb abortion at the local level. The campaign was part of a new strategy by anti-abortion activists to circumvent Democratic-controlled state legislatures. Albuquerque was seen as a test case, since it's a Democratic enclave with a large Latino (and thus Catholic) population that is home to New Mexico’s only two abortion clinics.

But like so many ballot measures that aim to stop abortion, this one failed by a wide margin — 55 to 45 percent — despite polling that at one point showed the referendum might succeed. It’s just the latest evidence that the anti-abortion movement is struggling to score victories at the ballot box, even as conservative state legislatures across the country have passed dozens of laws aimed at making it harder for a woman to get an abortion.

In 2011, voters in Mississippi, arguably one of the most conservative states in the nation, rejected a personhood amendment to its constitution that would have enshrined the idea that life begins at conception. A full 58 percent of voters were against it.

In 2008 and 2010, Colorado voters defeated personhood initiatives by roughly three-to-one margins. The residents of South Dakota overwhelmingly voted against banning abortion in 2008. Since 2005, a total of 15 ballot measures have gone before voters, and 13 of those have failed.

"We've seen time and time again when the issue is actually put before the voters that they defeat these attempts to ban or restrict abortion," said Gretchen Borchelt, senior counsel and director of state reproductive health policy at the National Women’s Law Center, a nonprofit based in Washington, D.C. "The voters see how extreme these measures really are."

Opponents of abortion have had much more success in red-state legislatures. Bans on abortion past 18 or 20 weeks have been enacted in 12 states, though three were suspended by the courts. Twenty-six states have laws that require women to wait at least 24 hours between when they receive counseling and when they have the procedure. Several more require that parents either be informed or give consent to minors seeking abortions.

In Texas, lawmakers have succeeded in shutting down several clinics by forcing abortion providers to have admitting privileges at local hospitals. Doctors are also required to show patients images from the ultrasound and make the fetal heartbeat audible. The new rules forced 12 of the state's 36 clinics to stop providing abortions.

But that doesn't mean the right-to-lifers are giving up on the referendum front. There are several ballot questions already being prepped for the 2014 midterms, including another personhood referendum in Colorado.

Whether any of the measures are successful remains to be seen. However, one thing is clear: If instead of proposing modest, incremental changes, these groups continue to push for extreme anti-abortion propositions, the evidence shows that voters just aren't prepared to go there.