A proposed Arkansas state law that that would ban women from getting an abortion more than 12 weeks into the pregnancy, could find second life in the state Senate after being vetoed by Gov. Mike Beebe on Monday.

On Tuesday, a Republican-led attempt to override Gov. Beebe's veto of the 12-week abortion ban began in the Arkansas state Senate, according to the AP.

In order for the override to be a success, a simple majority is needed in the state Senate and House of Representatives.

Last week, Arkansas lawmakers overrode the governor's veto of a ban on abortions more that 20-weeks into the pregnancy.

Unlike the 12-week abortion ban, the 20-week ban, which took effect immediately, does not allow exemptions for even highly lethal fetal disorders, on the controversial belief that fetuses can feel pain at that stage of the pregnancy.

Both bans allow exceptions for rape and incest.

Governor Beebe told reporters he finds the 12-week abortion ban more troubling than the 20-week bill.

"Both of them are constitutional issues. I don't know if you'd characterize one as easier than the other," Beebe told reporters. "It becomes a question of what is the constitutionality of the bill."

Republicans gained control of both chambers of the Arkansas legislature in the 2012 elections, for the first time since the Reconstruction Era. GOP lawmakers currently hold 21 of 35 state Senate seats and 51 of 100 House seats.

Arkansas Republican Senator Jason Rapert proposed the 12-week abortion ban.

He claims to be unfazed by Beebe's most recent veto, but confident GOP lawmakers will override it.

"It's not a surprise," Rapert said. "Given the opportunity to save lives of unborn children, this governor has always chosen this session to say no. I'm disappointed for all of the unborn children that could have been saved in this bill, but I have faith that the 70 percent of the Legislature that voted to pass the bill will be there to override this veto."