With just five days until Congress adjourns for summer recess, Sen. John Cornyn, R-Texas, and Rep. Henry Cuellar, D-Texas, are attempting a bipartisan, last-ditch effort to address the border crisis in their home state - but there are few signs of support in Congress.

"The American public wants us to have an orderly border," Cuellar told ABC News' Jonathan Karl on "This Week" Sunday. "They're seeing chaos at the border."

The Cornyn-Cuellar bill aims to change the existing 2008 law that differentiates between the process undocumented children coming from Central America and those coming from Mexico go through if they are returned to their home countries after entering the U.S. The proposed legislation would allow the U.S. to expedite the deportation process for migrant children from Central America, which is how the U.S. currently handles Mexican immigrants.

Despite the lack of strong support in favor of the proposal from congressional Democrats, Cornyn said he remains optimistic about House legislators using the bill as a potential guide for a solution, while acknowledging difficulties in the Senate.

"Fortunately it sounds like the House of Representatives is going to move a piece of legislation this week, which would actually offer a solution, and it will include something along the lines Henry and I have proposed," Cornyn said. "In the Senate, Senator Reid is - still opposes our proposed solution … My view is a solution beats no solution every day and nobody has offered an alternative, so I hope we will act."

When pressed to further acknowledge the lack of support from high-ranking elected officials on the left, Cuellar echoed Cornyn's optimism by noting the White House's efforts to find a solution to the crisis while stressing the need to evaluate the current conditions on the border.

"President Obama requested [cooperation] at the beginning; Secretary Johnson has been good, but again I represent the district. I don't just go down there once in a while and see what's going on, I live there." Cuellar said.

"Forty-two thousand of the unaccompanied kids out of the 58,000 have come through that small area, so we're at the epicenter," Cuellar continued, describing his district, which includes 200 miles of the U.S.-Mexico border. "The folks in the community have been dealing with this on a day-to-day basis. We need the resources and we also need a policy change."

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