The bill requires doctors to have admitting privileges at nearby hospitals, only allow abortions in surgical centers and ban abortions after 20 weeks.
Democrats and women's rights activists have protested the bill for weeks. The measure failed to win enough support during the regular session, then died in the first special session due to a 13-hour filibuster by state Sen. Wendy Davis, a Fort Worth Democrat.
Republican leaders, including Gov. Rick Perry and Lt. Gov. David Dewhurst, are intent on passing it quickly through the Republican-controlled Legislature in a second special session. Democrats can do little but slow the bill down, attract as much attention as possible and lay the groundwork for a federal lawsuit to block it once it becomes law.
Davis' successful filibuster put the Texas bill in the spotlight of the national abortion debate. On Monday night, former Arkansas Gov. Mike Huckabee spoke to abortion rights opponents. The Planned Parenthood Federation of America announced a statewide bus tour Tuesday morning, dubbed Stand With Texas Women.
"It seems like every time women looked up from doing their laundry of helping children with their homework, the Texas Legislature is right there taking aim at them again," said Cecile Richards, president of Planned Parenthood Federation of America. "Over the past few years, more than 50 women's health centers have been shut down."
Women from both parties who support abortion rights introduced a series of amendments to water down House Bill 2, hanging coat hangers on the front podium to symbolize illegal abortions, which they say will become more common if the law is enacted. Rep. Senfronia Thompson, D-Houston, called for an exception to the 20-week ban in cases of rape and incest, but Laubenberg rejected the proposal.
An anti-abortion voting record is critical to winning Republican primaries in Texas. Texas Alliance for Life, a Christian group that maintains a scorecard on lawmakers, sent out messages on Twitter opposing each amendment, signaling how lawmakers should vote for a high score.
Supporters of the restrictions insist that they will improve the healthcare women receive by placing more stringent conditions on abortions. Laubenberg told the House on Tuesday that her bill would ensure that women get high-quality treatment while protecting "babies" after 20 weeks of gestation.
"What we're talking about today truly is about the health and safety of a woman who would undergo an abortion, but also, I want to point out, we are talking about an unborn child," she said.
Federal courts have ruled that states can regulate abortions but not to the extent to make them impossible to obtain. That hasn't stopped Republican-led legislatures in Texas and several other states from passing laws in recent years that test the legal limits.
Opponents of the Texas restrictions say they would effectively ban abortion in much of the nation's second most-populous state by causing the closure of 37 of its 42 abortion clinics.
Houston Rep. Sarah Davis, the only Republican opposed to the law, warned that the bill as written is unconstitutional and she offered an amendment to make it less stringent.
"I believe the bill as drafted will be a de facto ban on abortion," she said. "No one wants to see abortions, it's a terrible way to end a pregnancy, but it is a constitutionally protected right."
They also say the Texas restrictions and those passed by other states conflict with the U.S. Supreme Court's 1973 Roe v. Wade decision, which established that a woman has the right to get an abortion until her fetus could viably survive outside of the womb, which is generally at 22 to 24 weeks of the pregnancy.
It's unclear if the Texas restrictions could survive a court challenge. Federal courts have suspended aspects of the bill passed by other states. On Monday, a federal judge blocked enforcement of a Wisconsin abortion law requiring admitting privileges.
The Texas Medical Association, the Texas Hospital Association and the American College of Obstetrics and Gynecology oppose the bill, calling it unnecessary.
The Texas Department of Public Safety has more than doubled the number of troopers at the Capitol due to the rallies and marathon hearings, said Sen. Kevin Eltife, a Tyler Republican who oversees the Senate Administration Committee. He declined to reveal the exact number of troopers or how much the boost in security cost.
Lawmakers told the DPS they wanted plenty of troopers on the ground no matter the expense, he added.