A key House Democrat involved in crafting a bill to deal with the border crisis said he might not support the final product if Republicans add what he sees as poison pills.

Rep. Henry Cuellar (D-Texas) told The Hill that he generally supports the recommendations that will form the basis of the GOP's border bill. Still, he says he won't vote for the measure if Republicans try to reverse President Obama's deferred deportation program for some people who came to the U.S. illegally as children.

"They'll lose me. For example, if they want to get rid of the DACA [Deferred Action for Childhood Arrivals] — the DREAM Act —  then that's a different thing. Then it's a problem with me," Cuellar said.

Cuellar has publicly criticized President Obama for not visiting the Texas border, where thousands of Central Americans have entered into the U.S. illegally.

House GOP leaders are seeking to vote on their border bill this week before leaving town for the August recess.