In a CBS interview broadcast Sunday, President Obama slammed approaches to immigration reform that he said "demagogue" a "national problem."

He also defended progress in the administration's lawsuit against Arizona's SB 1070 immigration law — an action stating that the controversial measure flouts the federal government's imperative under the 'supremacy' clause of the constitution. 

SB 1070 in its full implementation would require police to verify the citizenship of individuals they encounter if they have "reasonable suspicion" that one is an illegal immigrant. It would also make it a crime for illegal immigrants to seek work in the state.

Arizona Gov. Jan Brewer (R) responded last Thursday to a recent injunction against portions of SB 1070 by filing an expedited appeal to the Ninth Circuit. The Supreme Court may ultimately resolve the case.

Speaking with "Early Show" anchor Harry Smith, Obama criticized what he sees as political opportunism in Arizona's approach.

"What we can't do is allow a patchwork of 50 different states, or cities or localities, where anybody wants to make a name for themselves suddenly says, 'I'm going to be anti-immigrant, and I'm going to try to see if I can solve the problem ourself.' "

A CNN/Opinion Research poll released Wednesday revealed that 55 percent of Americans support SB 1070. Fifty-four percent say it will lead to discrimination of Latino Americans.

Another recent poll, limited to Arizona, shows that 65 percent support the law, while 27 percent don't.

Arizona Republicans have denounced the federal suit, saying the Justice Department is overstepping its sphere.

"Attorney General Holder speaks of the 'federal government's responsibility’ to enforce immigration laws; but what are the people of Arizona left to do when the federal government fails in its responsibility?" said Sens. John McCain (R-Ariz.) and Jon Kyl (R-Ariz.) in a July 6 statement.