White is trying to unseat Republican Gov. Rick Perry, who's seeking an unprecedented third full four-year term.
White said he wants to limit the governorship to two four-year terms. The former Houston mayor, in a written statement Tuesday, said there should be a voter referendum on the issue.
Perry spokesman Mark Miner said the governor disagrees. Miner said Perry trusts the voters to decide each election whether they want someone to remain in office.
White said Texas needs term limits to avoid the use of power by special interests to entrench a governor in office.
The election is Nov. 2.