Miller's major point of contention with the Senate bill is the two-hour lapse before the abortion, which Miller does not think is sufficient time for the woman to "talk to her friends and family, pray about it, and get a good night's sleep."
The state Senate's hard line is the exception for rape and incest, to which Miller responded that it's especially important for women in those situations to have all of the information available to them.
Perry indicated that he would sign the bill once the Senate and House vote on a final version.
The Associated Press contributed to this report. ABCNews.com reporter Reshma Kirpalani is a member of the ABC News on Campus program at the University of Texas in Austin.