I use a number of corporate rates and have never once been asked for a company ID or business card or anything to prove I'm eligible. The same for AAA. I actually show no ID at all at check-in besides my credit card. If a clerk asks me for ID I give them my MR number and, if needed, remind them that I booked on-line with the same credit card I've just handed them.

The cities mentioned are all fairly cheap. Maybe not downtown areas, but there should be plenty of properties around the $100 (plus taxes and stuff). $100 is really low for most corporate travel policies, by the way. Mine is $200 except for large cities and outside the US, where it's whatever that's reasonable. Some other companies are in the $150 range, some don't really have a hard limit but would certainly frown on stays at pricey hotels.

I stayed 77 nights this year and it was mostly at Fairfield, Residence Inn or SpringHill Suites. I don't recall ever paying under $100 for any stay. I don't think that budget and Marriott is going to be the right solution for you.

Over the last couple of years I've had about half nights that were in the $100 or less range. It just depends on the dates you're there or how far out of a given city you want to stay.

Manhattan on a Tuesday night? You won't get a bum's nest for $100.

Indianapolis IN on a Tuesday night? There's a Fairfield Inn with no special rate for $98. With AAA, multiple FIs under $100. With IBM's corporate rate, Res Inn, Courtyard, multiple Fairfields and a Townplace Suite under $100. That's within 10 miles of downtown Indianapolis.