In a move that will help Republicans pass legislation, the Texas Senate lowered the requirement of a supermajority from 19 to 18.
Formed as a response to growing calls to defund the police, Abbott brought his "Back the Blue" pledge to Houston.
Following a court decision on payment this week, divisions appear among prosecutors in the disputed case against Attorney General Ken Paxton on next steps.
The legislation will now head to conference committee as Texas moves one step closer to raising the legal age for purchasing tobacco products to 21.
