This would place a severe burden on Texas women wanting to exercise their right to control their own body -- forcing many to have to travel hundreds of miles to get to a clinic. That might not be bad for some women, but for the poor (especially those without their own transportation) it could be prohibitively expensive.
A request was filed with the 5th Circuit Court of Appeals to stay the law going into effect, but it was turned down. Plaintiffs then appealed to the Supreme Court. On Monday, the U.S. Supreme Court issued a temporary stay to allow the Texas clinics to stay open. The order gives plaintiffs time to prepare and file a petition for a hearing on the law before the Supreme Court. It's not guaranteed the court will then hear that petition, but it's very unlikely they would have issued the stay unless they were going to hear the case.
Roberts, Scalia, Alito, and Thomas opposed issuing the stay, while Kennedy (picturedP joined Kagan, Ginsburg, Breyer, and Sotomayor to allow the clinics to stay open. It looks like Justice Kennedy will once again be the swing vote when the case is heard. It's anyone's guess as to which way he will vote, but he did vote for the stay and has been unwilling to vote to overturn Roe vs Wade in the past.