Texas is a big state with a big population and with a higher than national average rate of right wing crackpots. So there are easily enough people willing to sign their petition.
This article explains what is happening.
The Republican party leadership is entirely against this. From the article:
But that hasn't stopped the Republican Party of Texas from rolling its eyes at the secessionists. Texas GOP communications director Aaron Whitehead said the Republican party certainly doesn't welcome outside groups trying to doctor the party ballot.
“Historically the executive committee of the Republican Party has chosen what goes on this,” Whitehead said, “and it’s party preference that it stays that way.”You would think the Republicans would be more emphatic and specific in criticizing a movement that is against the UNITED States of America.
The problem probably is that they don't want to give the secessionists free publicity, and also this is something the Republican Party base might be sympathetic to.
What must worry the Texas Republican leadership is that the percentage of Republicans who might be willing to vote yes on this could be embarrassingly high. Individuals might vote for it as joke, or an expression of opposition against Obama, or just to irritate the Republican leadership all thinking that their little protest vote won't matter that much.
Then when the results are tabulated the percentage that voted yes might be very high.
Also, the Democrats may well decide to encourage the yes vote to embarrass the Republicans. A leading Democratic figure might condemn the Texas Nationalist Movement which would encourage members of the Republican party base to vote for the Texas Nationalist Movement in a reflexive response.
Other tactics might be to have some group condemn Texas secession in a way that would drive people to vote for secession. For example, point out that LGBT rights wouldn't be safe in an independent Texas.
This can be a dangerous game to play. If the Texas Nationalist Movement gets a significant percentage it could very well give the secessionists credibility and get more people involved and then another ballot with an even higher percentage vote for secession.
Chances are now that they will get a percentage yes on the Republican primary to embarrass the Republicans, but the movement won't be able to achieve their goals and as Texas demographically changes it will be much less interested in secession.
However, the future is opaque to us. Sometimes the unexpected happens and in some crisis the Texas Nationalist Movement might be in a position where they have a good prospect of achieving their goals.
I think though that this will be all great laughs and the Republican Party will learn the lesson that being the party of crazy can have negative consequences.