No. Only government agencies (IRS, state tax boards, student loan dept.) can garnish wages. Even then, many types of federal benefits are exempt.
There's long process that happens before government garnishing occurs for back taxes, defaulted loans, etc. You'd be notified by mail and have an opportunity to appeal or make payment arrangements.
Credit card companies can report delinquencies and damage your credit rating; they cannot garnish. If they threaten you with garnishment, tell them you will report them to the Federal trade Commission and your state attorney general because it is illegal for them to threaten you with garnishment. Learn more at:
http://www.ftc.gov/bcp/edu/pubs/consumer/credit/cre18.shtm
Big love.