In response, Gov. Abbott threatened to hit the lawmakers where it hurts — their bank accounts.
"I will veto Article 10 of the budget passed by the legislature," the governor warned in a tweet, noting that "Article 10 funds the legislative branch."
"No pay for those who abandon their responsibilities," he said. "Stay tuned."
According to the Texas Tribune, Abbott has until June 20 to carry out the veto, which would affect state funding of lawmakers and their staffs starting Sept. 1. Funding of the legislative branch through the end of August is covered under the current budget.
The outlet noted that "state lawmakers are paid $600 a month, equal to $7,200 per year. They also get a per diem of $221 for every day they are in session, including both regular and special sessions."
Following Abbott's threat, Democratic lawmakers lashed out, criticizing the potential move as authoritarian.
Democratic state Rep. Donna Howard tweeted, "This would eliminate the branch of government that represents the people and basically create a monarchy."
Abbott reportedly added on Monday that he would call a special session of the legislature to pass the bill, though he did not specify a date when that would occur.
Similarly, Texas Republican House Speaker Dade Phelan defiantly stated, "We will be back — when, I don't know, but we will be back. ... There's a lot of work to be done, but I look forward to doing it with every single one of you."
The bill — which aims to protect elections against fraud in part by tightening rules surrounding early voting and mail-in voting — has been carelessly criticized by Democrats, including President Joe Biden, as an attempt to restrict voting access for minorities and low-income individuals.
The president lambasted the bill as "un-American" in a statement to the Texas tribune.
"Today, Texas legislators put forth a bill that joins Georgia and Florida in advancing a state law that attacks the sacred right to vote, " he said. "It's part of an assault on democracy that we've seen far too often this year — and often disproportionately targeting Black and Brown Americans."