DALLAS (CBSDFW.COM) - Governor Greg Abbott's comments on the new fetal heartbeat law received national attention, but perhaps not the reaction he was looking for.

After he signed the elections integrity bill into law Tuesday, Sept. 7, Gov. Abbott was asked why rape and incest victims weren't exempt from the new law and had to carry their pregnancies to term.

Gov. Abbott said, "It provides at least six weeks for a person to be able to get an abortion.. Rape is a crime. And Texas will work tirelessly to make sure that we eliminate all rapists from the streets of Texas."

Dr. Allison Campolo, Chair of the Tarrant County Democratic Party called his answer and similar comments from other Republicans enraging. "They are so out of touch with people on the ground."

Campolo criticized the law that went into effect Sept. 1 because it prohibits abortions once a fetal heartbeat can be detected, which can be as early as six weeks, when many women don't know they're pregnant and because exceptions are made only for medical emergencies.

She also went after Governor Abbott's comments.

"His comments specifically about rape, in terms of rape victims can get an abortion, and we're going to eliminate all rape in Texas, are really outlandish. You know, if this Governor has been sitting on a plan to eliminate rape in Texas, why hasn't he done it?"

Cathie Adams, National Board member of the conservative group Eagle Forum criticized Abbott's remarks for different reasons.

"It's not going to be something easily forgotten," she said.

Adams, a former Texas GOP Chair, said while she's glad Gov. Abbott signed the law, his comments defending life fell far short.

"He says, and we agree that life begins at conception, and if that be true, we don't need to be using the first six weeks of a pregnancy in order to terminate it in order to end innocent life."

Governor Abbott faces a primary challenge from two conservatives, Allen West, a former Texas GOP Chair, and Don Huffines, a former State Senator from Dallas.

After Abbott's remarks Tuesday, Huffines issued a statement saying, "It is disgusting to watch our Governor tout his pro-life credentials while advocating for women to get abortions in the first six weeks of pregnancy."

Matthew Wilson, a SMU Political Science Professor, said Governor Abbott could have done a better job answering the question.

"Getting fire from both sides is a bad place to be politically," said Wilson.

Wilson said because Gov. Abbott signed the heartbeat bill into law, he still has substantive credibility among those who are pro-life.

He said Abbott's remarks may prove more costly among not only Democrats but Independents, too.

"There will be some damage to Governor Abbott that comes out of this. The danger will be the portrayal in a general election context, that he is somehow out of touch or insensitive when it comes to questions to rape."

No major Democrat has announced yet a run for governor.

Campolo said, "I'm not sure that the governor's comments will be what spurs anybody to action, although, we can hope that maybe this is the straw that initiates a big name to run."