Crown-sourcing the legal brains and/or the ones here who are really good at looking up this kind of stuff...

So tomorrow, fuckwit Rick Perry's new legislative session begins, and the first thing they're going to do is take up SB5, and I'm expecting that despite everyone's best efforts, it might pass. My question is, though, is there a way to appeal it? Like, can pro-choice groups or whoever sue to keep it from being implemented, and thus tie it up in the court system for a time, maybe years, to come?

I honestly am not being lazy about asking this if this is something I can google, but to be honest, I've been cooking the last 3 hours and I like to drink wine while I cook so I'm a little bit toasted right now but holy cow did I just make the best Shepherd's Pie ever (secret: a good glug of Merlot into the meat mixture). (also, I know it's not really the kind of food you'd cook when it's a jillion degrees out but that's why I keep my central AC to 70 degrees in the summer and I don't care).