The not-exactly-in-depth L.A. Times article "Banking on illegal immigrants" by E. Scott Reckard, David Streitfeld and Adrian G. Uribarri discusses the backlash to Bank of America's credit card for illegal aliens. It informs us:

"At face value the program seems to be problematic," said Russ Knocke, a [Department of Homeland Security] spokesman. "It seems to be lending itself to possibilities of perpetrating identity theft or creating more risk for money laundering."

...[Rep. Tom Tancredo] said he sent a letter to U.S. Atty. Gen. Alberto R. Gonzales and Department of Homeland Security Secretary Michael Chertoff asking them to look into the program.

"I hope the administration will shut down this reckless and illegal program before Bank of America extends a line of credit to a potential terrorist," said Tancredo, a hard-line foe of illegal immigration...

Then, almost at the bottom of the article, we're treated to the news that another bank knows exactly who it's dealing with:

Since then, Wells has opened more than 1 million accounts for Mexicans using the consular card. It also accepts Guatemalan, Argentine and Colombian identity cards. The assumption is that most immigrants using the cards to identify themselves are here illegally, Wells Fargo spokeswoman Trigg said, but the bank doesn't ask.