H.P.
All of the daycares I checked into when I was pregnant had a waiting list so I'm not sure what providers you are talking to. My son has been in various daycares in your area/Westchase & westshore. The problem is that not many takes infants or are very expensive. As for finding a place close to work, the only one that met my standards was Time of Wonder on Eisenhower (I work in Westshore too). They take infants and I'm sure have a waiting list. Though it wasn't my first choice, it was the best for the price. The centers in Westchase were too expensive at the time.
Even if you are told the center is booked, still put your name on the waiting list. Many parents find other care before they get a call, so your name might get bumped up on the list.