They would need to have another session to vote to override the veto. So they'd also need a mechanism to reconvene, given they are only in session for 140 days every other year.
By extending that session or adding another, the legislators would need more time off from their other jobs potentially at a pay cut. Legislator are only paid for time in session.
Sessions only take place for a few months every other year. To override a veto from Abbott in July 2025, the legislature would need to wait until early 2027. In order for the legislature to act more quickly to override a veto, they would need the power to call a session or there would need to be rules added to address the vetoes that take place after the legislative session is over. I suppose the governor could be given a deadline to sign, veto, or refuse to take action on a bill a certain number of days after the conclusion of a session and the legislature could have a mini session to discuss the bills that were vetoed or where action wasn't taken for a predetermined amount of time after the governor's deadline.
The governor has the power to call a special session between normal sessions to address issues. Those issues are supposed to be outlined before the special session starts. Obviously he's not going to call a session to address a bill that was vetoed unless it was maybe vetoed over a couple small points.