Republicans who favor tougher border measures say the border has been dangerous for years as illegal immigrants flow into the country through Arizona, New Mexico, Texas, and Southern California. But Rep. Beto O'RourkeĀ  (D-Texas) said border cities in his district are entirely safe.

"In fact, the community I represent, El Paso Texas, is the safest city in the United States, bar none," he said. "It was the safest city last year in the United States, and the year before that."

"The U.S. side of the U.S.-Mexican border is safest place to be anywhere in the United States today," he added.

He and other Democrats said they oppose tougher border measures for several reasons, including that it would destroy the culture of towns along the border. Rep. Filemon Vela (D-Texas) said more fencing would drive a wedge between border communities that are "culturally united."

"The current border fence has come to symbolize divisiveness and serves as a daily reminder of a flawed immigration system," he said. "For this reason, residents on both sides of the border oppose the border fence."

Vela added that more fencing would "damage already fragile wildlife and natural resources," and said it would cost billions to build, money that could be better spent to help communities.

Rep. Pete GallegoPete Pena GallegoTexas Democrats smell blood in the water for 2018 ObamaCare repeal vote: 15 GOP lawmakers to watch Vulnerable Texas GOP lawmaker survives rematch MORE (D-Texas) agreed that money for additional fencing would be better used, but he suggested shoring up infrastructure to help facilitate trade.

"I'm opposed to the notion of a border fence, and would rather that we shore up our ports to speed up commerce," he said.

Democratic opposition to border measures in the Senate bill is something that could theoretically delay House consideration of the bill, except House Republicans are unlikely to bring up that bill as passed by the Senate. House GOP leaders are instead expected to call up their own border enforcement measures in the coming weeks.