The "Preservation of Sovereignty and Marriage Act" by Magnolia Republican Rep. Cecil Bell Jr. was heard Wednesday.
The proposal says no state or local funds could be used to "license, register, certify or support" gay marriage. The measure would also prohibit officials from recognizing, granting or enforcing gay marriage licenses.
Justices will hear same-sex marriage arguments this summer. Bell's bill aims to ensure that, regardless of their ruling, gay marriage would remain illegal in Texas.
In 2005, voters statewide passed a constitutional amendment banning gay marriage.
Bell says this is about the sovereignty of the states.
Mark Phariss, a Plano lawyer and same-sex marriage advocate, says if passed, he feels it would be ruled unconstitutional.
"This really is an effort to try to the best they can, undo the best they can, the protections we've been given under the federal Constitution, and that's just wrong," said Phariss.
Ahead of Wednesday's committee hearing, opponents of same-sex marriage rallied in front of the Capitol on Monday. The keynote speaker was Roy Moore, the Chief Justice of the Alabama Supreme Court who ordered judges not to issue same-sex licenses or fear losing their jobs.
The Associated Press contributed to this report.