Then legislative positions would be even more inaccessible to those not already wealthy.
TX legislative pay is $7,200 per year plus a per diem of $221 while in session.
"Therefore, the total compensation for a regular session would be $38,140 ($7,200 base + $30,940 per diem). Over a two-year term, the total pay is typically around $45,340 ($7,200 base pay x 2 years + per diem for one 140-day regular session). This relatively low base pay highlights that the legislators’ roles are often viewed as part-time public service rather than full-time career positions."
https://www.ncesc.com/geographic-faq/what-is-the-salary-for-texas-legislators/
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.