AUSTIN, Texas — When Texas’ new abortion law made no exceptions in cases of rape, Republican Gov. Greg Abbott defended it with an assurance: Texas would get to work eliminating rapes.

One year later, Lindsey LeBlanc is busy as ever helping rape victims in a college town outside Houston.

“The numbers have stayed consistently high,” said LeBlanc, executive director of the Sexual Assault Resource Center in Bryan, near Texas A&M University. Despite hiring two additional counselors in the past six months, she still has a waitlist for victims.

“We are struggling to keep up with demand,” she said.

The constant caseloads in Texas are another example of how Republicans have struggled to defend zero-exception abortion bans that are unpopular in public polling, have caused uproar in high-profile cases and are inviting political risk heading into November’s midterm elections. A year since Texas’ law went into effect in September 2021, at least a dozen states also have bans that make no exceptions in cases of rape or incest.

The absence of exceptions has caused divisions among Republicans, including in West Virginia, where a new law signed this month allows a brief window for rape and incest victims to obtain abortions only if they report to law enforcement first. Recently, South Carolina Republicans scuttled a proposed ban after failing to get enough GOP support.

“It really disgusts me,” said Republican South Carolina state Sen. Katrina Shealy, ripping into her male colleagues on the floor of the state Senate.

Republican U.S. Sen. Lindsey Graham, also of South Carolina, allowed exceptions under the proposed national abortion ban he introduced last week. The proposal has virtually no chance of passing, with even GOP leaders not immediately backing it, reflecting how Republicans have broadly struggled to navigate the issue of abortion with voters since the U.S. Supreme Court overturned Roe v. Wade this summer.

Overwhelming majorities of voters think their state should generally allow abortion in specific cases, including rape, incest or if the health of the pregnant person is endangered. Even Republicans are seeing it as a line with some voters.

“It’s a very gray issue,” said Claudia Alcazar, the GOP chairwoman in Starr County along the Texas-Mexico border that has become a new political battleground after Republicans made big gains with more conservative Hispanic voters in 2020.

She said she knows those who are “hardcore, never have abortion for any reason, period. And then I have the other ones that are like, ‘Well, you know, it depends.'”

In Texas, the blowback was swift when Abbott said last September: “Texas will work tirelessly to make sure that we eliminate all rapists from the streets.” Critics called it detached from reality. A sexual assault hotline in Houston has answered almost 4,800 calls through August this year — putting it on track to exceed last year’s volume of 4,843.

As of this summer, all abortions were banned in Texas except if it would save a mother’s life.