Yet more Democrats are piling on President Barack Obama for skipping a visit to the U.S.-Mexico border during his recent trip to Texas.

"I wish he would have come to the border,' said U.S. Rep. Beto O'Rourke, a Texas Democrat. "It would have sent an important message to the rest of the country about how seriously he takes this issue beyond the spending request he sent to Congress last week."

Obama's decision to skip the border comes as more and more unaccompanied immigrant minors are making their way in the United States, creating what both Democrats and Republicans have called a humanitarian crisis. Obama has requested $3.7 billion in emergency funding to help ease the burdens on federal officials and facilities, as well as to crack down on smugglers.

While in Texas, Obama pressed for Congress to give him the funds and met with Republican Gov. Rick Perry. But border state politicians continue to say Obama missed an opportunity to see the crisis first hand.

"I wish he would have come to my district of El Paso where we've seen thousands of family members," O'Rourke said. "I wanted him to meet the men and women of the border patrol, of [U.S. Immigration and Customs Enforcement], of Annunciation House, a Catholic charity that's helping to take care of these families and reunite them."

"The President should have gone down there," Democratic Rep. Luis Gutierrez of Illinois told CBS's Bob Schieffer.

White House press secretary Josh Earnest says Obama's focus has been on the issue, rather than on his image.

"The President's priority was on solving the problem," Earnest said. "The President's putting the policy solution first, even though he's been criticized over photo ops. That's leadership and that's what the President's been focused on."

And while Gutierrez said he would have liked Obama to make the trip, he made clear where he thinks the blame lies in the broader legislative battles over immigration reform.

"The administration has been trying to work with Congress to pass an immigration reform bill for over two years," Gutierrez said. "So it's been folks in Congress and specifically in the House of Representatives who have not moved forward on a bill that would have helped us prevent some of the things we're seeing on the border now."

Texas Democrat Rep. Joaquin Castro praised administration officials who have made the trip. While he didn't offer any additional details, Castro said not to count out a border visit from Obama in the future.

"The fact is, this was not the President's last opportunity to get to the border. I think you will see him go down there. I think it's important for him to get down there at some point, to let people know he personally is attending the situation," Castro told NBC's David Gregory. "[Homeland Security Secretary] Jeh Johnson has been down there five or six times. He's keeping the President apprised of everything."