AUSTIN, Texas (CBSDFW/AP) – Texas Democratic lawmakers (who blocked what they consider one of America’s most restrictive voting measures with a walkout) sued Republican Gov. Greg Abbott on Friday, after he vetoed funds that cover thousands of Capitol paychecks that he said shouldn’t be given “to those who quit their job early.”

The lawsuit reflects the tensions that remain in Texas more than a month after Democrats’ last-ditch revolt over the Memorial Day weekend, and more battles are ahead. Abbott has ordered lawmakers back on the job for a special session starting July 8, when Republicans are expected to embark on a second try at passing new voting laws.

READ MORE: Southwest Airlines Employee Sentenced 6 Months For Stealing Guns From Bags

Going straight to the Texas Supreme Court, Democrats called the veto an unconstitutional power grab. Abbott has indicated he will give lawmakers the chance to reinstate the money once they return for the special session.

The veto of more than $400 million in funds didn’t just punish Democrats: paychecks for the offices of Republican legislators are also impacted, as well as nonpartisan support staff around the Capitol. Democratic state Rep. Chris Turner put the number of affected jobs in the legislative branch at more than 2,000.

“Governor Abbott’s position – that he is able to defund a co-equal branch unless or until it bends to his will – contains no limiting principle,” the lawsuit reads.

Abbott’s office did not immediately return a request seeking comment.

In his veto proclamation, Abbott wrote: “Funding should not be provided for those who quit their job early, leaving the state with unfinished business and exposing taxpayers to higher costs for an additional legislative session.”

The vetoed funding only applies to the next budget cycle that begins in September, meaning paychecks for Capitol staffers will continue at least until then. Lawmakers make just $600 a month in Texas – where the Legislature only meets for five months every other year – and many have well-paying careers back home. But Democrats say the veto puts at risk legislative staff whose jobs are their main source of income.

READ MORE: E.G. Daily On 'Rugrat's New Holiday Special "Traditions": 'We Embrace Everyone And Everything'

It was unclear when the court might take up the lawsuit.

Democrats are girding for another fight over voting this summer. Abbott and Republican leaders have promised to deliver new election laws in Texas, which already has some of the nation’s toughest voting restrictions, but have given little indication of what the next proposals might include.

The walkout by Democrats in May unfolded after nightfall as Republicans raced to pass a sweeping voting measure, known as Senate Bill 7, before a midnight deadline. Democrats say they were especially galled at last-minute changes to the bill that included a prohibition on Sunday morning voting – a time widely used by Black churchgoers – and provisions that could make it easier for a judge to overturn an election.

Republicans’ commanding majority in the Texas Capitol means an elections bill will probably eventually pass, but Democrats have vowed to continue fighting GOP efforts to reduce polling hours and ballot access. Nationwide this year, Republicans have rushed to enact a wave of strict voting laws in response to former President Donald Trump’s false claims that the 2020 election was stolen from him.

In Washington, D.C., a sweeping attempt by Democrats to rewrite U.S. election and voting laws was blocked this week by Senate Republicans, leaving Democrats with no clear path forward.

WATCH FULL INTERVIEWS WITH STATE REP. CHRIS TURNER AND STATE SEN. KELLY HANCOCK

MORE NEWS: Court Orders Full Review Of Texas Ruling That Blocks Biden Administration Arrests, Deportation Guidelines