"It's a federal problem," he said Wednesday in a meeting with the editorial board of The Salt Lake Tribune.
He said he realizes the federal government needs to find a solution.
Cannon, a six-term Republican, pointed to the December 2006 immigration raids at Swift meat-packing plants, including one in Hyrum, Utah, calling them "inappropriate." Some 150 Latino undocumented workers at the Hyrum plant were arrested and many were deported.
He characterized the move as political.
"The Republicans planned it for October so they could say 'Vote for me, I'm tough on immigration.' But then it didn't happen until December, so they ruined people's Christmas," said Cannon.
What also angered him was the fact that before the raid Swift had been fined $200,000 for "asking too many questions of Hispanics" and instead tried to use the federal Basic Employment Verification Pilot Program to attempt to identify undocumented workers.
They were raided anyway, and it cost them $30 million, he said.
Cannon brought up this fact to Homeland Security chief Michael Chertoff when Cannon visited the U.S.-Mexico border last summer.
The reply he received from Chertoff?
"That program doesn't work," said Cannon, adding he was shocked at the response.
Cannon worries that raiding only certain businesses, and often putting them out of business, will lead to graft.
"Arbitrary, capricious enforcement of a law results inexorably in corruption," he said.
But Cannon also is cautious to implement a program that does work, such as fingerprint identification for any job applicants, because it could infringe on civil liberties.
"Do we want to identify them? Then we would paralyze business," he said.
He worries about "shutting out" the 14 million or so undocumented workers from the economy.
"Do we want to keep them out of Wal-Mart? From buying shoes at the mall? From buying homes?" he asked. "We shouldn't destroy the economy by removing them from the economy."
Cannon was a key supporter of President Bush's failed immigration-reform proposal, which would have established a pathway to citizenship for undocumented workers.