A Democratic lawmaker from a district bordering Mexico concurred with Republicans Wednesday in saying border security must precede comprehensive immigration reform.

Rep. Gabrielle Giffords (D), who represents Arizona's 8th congressional district, which borders Mexico, said border security must be the first priority for lawmakers and President Barack ObamaBarack Hussein Obama Obama backs Trudeau in Canadian election Former Sen. Heller to run for Nevada governor Overnight Energy & Environment — Presented by Climate Power — Senate Democrats ding Biden energy proposal MORE and his administration.

"First and foremost, we have to secure the border," Giffords said during an appearance on CBS's "Washington Unplugged" webcast. "I really don't believe at this point, in the national dialog, we're going to have a comprehensive bill until we really, finally secure the border."

Giffords, a second-term lawmaker, had goaded Obama into agreeing to send 1,200 National Guard troops to the border in the state, mirroring a GOP proposal but still well short of the 3,000 troops Arizona Republican Sens. John McCainJohn Sidney McCain20 years after 9/11, US foreign policy still struggles for balance What the chaos in Afghanistan can remind us about the importance of protecting democracy at home 'The View' plans series of conservative women as temporary McCain replacements MORE and Jon Kyl had requested.

The Democrat is considered somewhat of a centrist, and said that she still supports comprehensive immigration reform, which would give illegal immigrants a path to citizenship. But, like many Republicans, Giffords said that securing the border is the first priority.

'I agree, and many of us in Arizona — Congressman [Jeff] Flake, Sen. McCain, and Sen. Jon Kyl, myself — have advocated in the past for a comprehensive immigration reform bill," she said. "I think we need do it, for a lot of different reasons. But we have to secure the border first."

"And that means all discussion about national security — and I serve on the House Armed Services Committee — the billions that we send abroad, we have to protect the United States," Giffords said. "National Security means border security."

Watch CBS News Videos Online