Updated at 4 p.m. with a letter from the Texas Democratic delegation responding to one from Gov. Greg Abbott.

WASHINGTON — House Democrats from Texas sent Gov. Greg Abbott a letter Thursday challenging his assertion that they are to blame for a lack of progress on immigration reform.

"It is disappointing to see our governor make the reckless and baseless assertion that it is our Texas Democratic Caucus who is refusing to take action on these issues," they wrote. "A basic Google search will reveal precisely which caucus is working to address challenges related to our Southern border and which caucus is stonewalling any honest effort to do the same."

Abbott had sent the Democrats a letter Tuesday asking them to support two Republican immigration bills scheduled for votes Thursday. "This is your moment," he wrote. "Seize it."

Every Texas Democrat refused to back the legislation, on which they were not allowed to give input. The more conservative of the two bills failed, and the vote on the other was pushed to next week.

In their letter to Abbott, the Democrats said the bill represents a compromise only among Republicans and used the opportunity to take a shot at the governor.

"As someone who has spent more than $1 billion in an effort to improve border security with very little positive results to show for it, we know that you understand how complex this issue is and the importance of working together to realize real results," the letter read.

Most of the Texas Democrats had co-sponsored their own legislation, the Keep Families Together Act, which prohibits almost all family separations at the border and limits criminal prosecutions for asylum seekers.

Trump's executive order

On Wednesday, the Texas Democrats expressed disappointment with the executive order President Donald Trump signed to stop the family separations, saying it didn't go far enough.

The order directs Attorney General Jeff Sessions to file a request to alter the so-called "Flores settlement agreement" — a 1997 court ruling that prohibits the government from holding undocumented children for extended periods. A 2015 ruling clarified that by setting a 20-day cap. Changing the agreement would allow families to be detained together "throughout the pendency of criminal proceedings," according to the order.

The administration hasn't been clear about whether or not the 2,300 children who have already been separated from their parents will be reunited with them while the adults are in federal custody awaiting immigration proceedings.

"It is still very early, and we are awaiting further guidance on the matter. Our focus is on continuing to provide quality services and care to the minors," read a statement from the Administration for Children and Families, a division within the Department of Health and Human Services. "Reunification is always the ultimate goal."

Rep. Sheila Jackson Lee of Houston had first heralded the order as a victory for the kids. "We won for the children," she said on social media, though she added that the order wasn't necessary given that Trump could have "picked up the phone" to end the separations.

We won for the Children. Not Trump. Today's result was due to all who prayed, traveled to the border, spoke out & those who keep fighting-We won for the children-This E.O. order was not necessary @Potus could have picked up the phone and & have ended it! #ikneel #NotInMyName — Sheila Jackson Lee (@JacksonLeeTX18) June 20, 2018

Later, after hearing that the fate of those already separated was uncertain — which she called a "reversal" on Twitter — Jackson Lee took the House floor with a different message: "This is a tragic executive order. It has no heart to it."

"Yes, it keeps the families together in a criminal posture and houses them in the same conditions, now on military bases, rather than allowing them to proceed through court proceedings, even though in my Southern District in Texas we are 50,000 cases in backlog," she said. "This executive order is not worth the paper it is written on."

Rep. Vicente Gonzalez of McAllen shared the concern for the families who have been affected by the zero-tolerance policy.

"There are several thousand children that have been separated that this executive order doesn't address, so it's still a concern," he said on C-SPAN on Thursday morning. "But I'm happy we're moving in the right direction."

Rather than a step forward, Rep. Marc Veasey of Fort Worth called the order the start of a new crisis. "The EO is not a real solution for families seeking asylum at the border," he said Wednesday on Twitter. "[With] the continuation of zero-tolerance, Trump plans to detain families & children indefinitely."

Time to get the facts straight:



•The Executive Order doesn't fix the crisis happening on our border.

•W/ the continuation of zero-tolerance, Trump plans to detain families & children indefinitely.



.@realDonaldTrump pretends to end one crisis while starting a new one. — Rep. Marc Veasey (@RepVeasey) June 20, 2018

Rep. Beto O’Rourke of El Paso, who is challenging Sen. Ted Cruz in November, denounced the prospect of indefinite detention, urging his Twitter followers to “refuse to be a nation that indefinitely locks away these families in cages for doing what any of us would do for our own children.”

"Looking at this executive order, how does it reunite kids with their parents?" he asked.

We marched, called, stood up and spoke out because we believed America to be a place that doesn't take kids from their moms and dads. But we also believe America to be a place that doesn't indefinitely detain families & children in camps. If we don't continue to act, it will be. — Beto O'Rourke (@BetoORourke) June 20, 2018

Reps. Joaquin Castro of San Antonio and Eddie Bernice Johnson of Dallas joined their colleagues in demanding immediate reunions for families already kept apart. "Those separated must be reunited," Johnson said.

We need a way to verify that separated children are reunited with their families. #KeepFamiliesTogether — Joaquin Castro (@JoaquinCastrotx) June 20, 2018