All states have deadlines for independent presidential candidates to file ballot access petitions that range from June 9 to September 9, 2016; except that the Texas independent presidential petition deadline is May 9.
The U.S. Supreme Court said in Anderson v Celebrezze, in 1983, that independent presidential petition deadlines cannot be as early as March 20. Since then, most states have moved their deadlines to July, August or September. Only four states are in June. Lower courts have invalidated June deadlines in Alaska, Arizona, Idaho, Kansas, Nevada, and South Dakota.
Thus, it seems likely that if any independent presidential candidate challenged the Texas May deadline, he or she would win. The Texas presidential independent deadline is even more difficult to defend because the Texas petition deadline for independent candidates for office other than president in 2016 is June 23 (30 days after the runoff primary). Obviously, if Texas election officials can cope with a late June petition deadline for independent candidates generally, there is no need for an early May petition deadline for presidential independents.
The Texas legislature doesn’t sit in even years, for the purpose of ordinary law-making. And the 2015 session adjourned months ago. Thus it won’t be possible for the legislature to fix the problem until 2017, unless there is a 2016 special session.