There was actually a serious attempt in the last (democrat controlled) congress to ban employers from considering an prospective employees criminal record unless they could demonstrate that the conviction would have a direct link to the job I.E. Child Molester/School Janitor. So basically employers could be sued for discrimination if they refused to hire a convicted criminal and the burden of proof would be on them to demonstrate the conviction was relevant to the job. Also, as I recall, part of the legislation was a ban on the use of credit checks for hiring purposes. Credit checks, according to the democrats are used as back door discrimination against minorities which tend to have lower credit ratings.
So, if this had become law, a bank could have been forced to hire a teller who was a convicted felon that is behind on all his bills and being chased by creditors. (no incentive to steal there...)
I believe some municipalities have already eliminated the question on employment applications about criminal histories. Pittsburgh, I recently read, is one of them.