Yes--at least regarding some parts of it.
One provision allows a suit to be dismissed early in the litigation process--perhaps, depending on the implementing rules, pursuant to a motion similar to the FRCP's 12 (b) (6)--and, if such a case is so dismissed, gives the trial court discretion to require the losing plaintiff to pay the attorney fees of the winning defendant.
Another provision states that the loser of a breach of contract case--whether it be the plaintiff or the defendant--will be required to pay the attorney fees of the winner.
The problem with those two provisions is this: the U. S. Supreme Court has held that the filing of a lawsuit is protected, at least to some degree, under the First Amendment right to petition the government for redress. Professional Real Estate Investors, Inc. v. Columbia Pictures, Inc., 508 U.S. 49 (1993). In that case, the Supreme Court was dealing with the "sham" exception to the general rule of immunity with regard to the filing of antitrust cases. Nonetheless, it is clear that its reasoning would apply to the filing of any lawsuit. That was recognized recently by the Federal Circuit in Ilor, LLC v. Google, Inc., 631 F.3d 1372 (Fed. Cir. 2011). In Ilor, the Federal Circuit was dealing with the patent statute that allows fee shifting against a losing patent plaintiff in "exceptional cases."
These two cases effectively hold that a plaintiff, under the First Amendment, cannot be punished for filing a lawsuit--by fee shifting or the imposition of other liability--unless the lawsuit is "objectively baseless." "Objective baselessness" was defined to mean that "no reasonable litigant could realistically expect to succeed on the merits."
The requirement that the plaintiff's case be objectively baseless--in order for the plaintiff to be ordered to pay the attorney fees of the defendant--creates a Constitutional threshold that applies to all statutes and rules that allow for the possibility of fee shifting against the plaintiff, such as FRCP 11, TRCP 13, and Chapters Nine and Ten of the Texas Civil Practice and Remedies Code.
And, of course, it would also apply to the Texas Legislature's "loser pays" bill, if it were to become law. Moreover, in the Professional Real Estate case, the Court spoke through a majority of seven, including all the conservatives.
I believe that Texas--with the rules and statutes that it currently has in place to discourage frivolous litigation--has already reached the Constitutional limit of what can be done in this area. Attempts to go further will be problematic.