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Currently, Texas is one of 14 states which have no limits on the amount of time a state official can sit in office.

"We have an obligation to make sure we elect citizens who want to serve, not politicians looking to build a career," George Seay with Texans for Term Limits said. "We put a man on the moon in eight years. If you can't get enough done in eight years in one particular job, I question how urgent your need is to further the common good."

The idea is that increased turn-over means less influence from lobbyists and interest groups, and more representation from voters across the state.

Legislation to limit terms has already been filed in both the House and Senate.

"The reality is, if you've got a fixed period of time of eight years to go in and pass your initiatives, your focus is going to be on a policy side, instead of a political side," Republican Rep. Lyle Larson from House District 122 said.

Rep. Larson is behind a bill which doesn't just put a cap on term limits. He said he'd also like to see legislation pass that would require a state official to resign from their post if they have more than a year left and are seeking higher office.

"We have folks going across the country, across the state, they essentially vacate their office,” Rep. Larson said. “We need to have people who are running the state's business in those offices."

If the term limit bill passes both chambers with a two-thirds vote, it would be up to voters in November to change the state’s Constitution to put a cap on term limits.

When Texans for Term Limits was asked whether the formation of the group was sparked by a particular politician—for example Governor Rick Perry, who's now serving his thirteenth year as governor—and the group said no.

Opponents say the rule would limit a voters' right to elect who they want to represent them.