Supported it is being done in around eight days: http://www.raceacrossamerica.org

There are also tours that will get you across in a month: http://www.pactour.com/

Those would both be on aggressive side if you weren't supported and at least had minimal amounts for credit card touring. After that point it will depend a bit on both the person doing the ride and your own preferences and styles. For example, how much of the time do you want to spend on the bike, are you looking for rest days, etc.

It wasn't quite credit card touring (I carried a tent and other camping gear) but my first trip across the US I did in five weeks averaging 95 miles per day including my one rest day. I wasn't particularly fast, but spent long days in the saddle. My second trip across the US was a month and a half and averaged 75 miles per day and was more comfortable in other dimensions. It can be done faster (eight days!) but you definitely need to work through your abilities, styles and preferences.