"As soon as they come back in the state of Texas, they will be arrested, they will be cabined inside the Texas Capitol until they get their job done," he said. "Everybody who has a job should show up to do that job."
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Democrats are attempting a showdown over how Americans are allowed to vote. They left Austin just days before the Texas House of Representatives were expected to give approval of new voting restrictions in a special legislative session.
MORE: TX Democrats aim to 'do what's best for constituents' during special session
The numbers meant the House would not have enough lawmakers in attendance to conduct business and vote on the bill.
"Minutes ago, at least 57 letters were delivered to the House general clerk directing the House to lock our voting machines and not unlock them until we provide expressed permission to do so upon our return to the Capitol," said Chris Turner, the chair of the House Democratic Caucus.
The Texas bill would outlaw 24-hour polling places, ban ballot drop boxes used to deposit mail ballots and empower partisan poll watchers.
Democrats argue getting rid of drive-thru and 24-hour voting methods will make it harder for young people, people of color and people with disabilities to vote.
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"We have not seen this level of retrogression in the right for people to cast their votes since the 1960s, and people need to do something about it," said one of the Democratic lawmakers at a briefing in D.C. "We are not going to stop. We are always going to push back against bigoted, racist, Jim Crow 2.0 style voting laws."
Rep. Toni Rose said House Bill 3 is making it harder for Texans to cast a "free, safe and equal vote."
She argued Abbott is demanding spotlight on everything except his failures.
"He has done nothing to protect the electric grid," Rose said.
Abbott said he will simply keep calling special sessions until elections next year, if necessary.
When asked what he is prepared to do if Abbott calls special session after special session, Turner said the Democrats' intent is to "stay out and kill this bill."
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Also in attendance on Tuesday's briefing was Rafael Anchia, who said Abbott poisoned the process.
"It was poisoned by a governor who defunded the legislative branch in violation of both the state constitution and also what has been developed by the U.S. constitution," said Anchia.
For weeks, Democrats have signaled they were ready to draw a line. Adding to their anger: A Houston man who gained attention last year after waiting more than six hours to cast a ballot was arrested on illegal voting charges a day before the special session began Thursday. Attorneys for Hervis Rogers say the 62-year-old did not know that his being on parole for a felony burglary conviction meant he wasn't allowed to vote.
Vice President Kamala Harris applauded Texas Democrats for their "courage and commitment" before they boarded the flight. Back in Texas, Republican Lt. Gov. Dan Patrick signaled that he would still try to pass a voting bill as early as Tuesday in the Senate. It was unclear whether Democrats in that chamber would continue showing up.
SEE RELATED STORY: 'This is a now-or-never:' Texas Democrats leave state to try to stop GOP voting bill
The Associated Press contributed to this report.