I typically travel with less than a week's notice and always find "acceptable" fares even the day of travel. Your best bet is to scour the main websites i have listed below. If you are just buying airfare, then you should purchase directly through the airline, especially if you have a frequent flyer's account. If you are buying a package, then you should book with the website.
If you are flexible on your dates, then you can save money. Also consider flying into nearby airports, up to 100 miles away. Most times there is cheap ground transportation to the main city center.
I have experienced that sometimes, booking hotel and air is cheaper than just air alone. One time when i flew from austin to chicago, the cheapest air i could get was 600 and that was on any website with any airline. i then booked through travelocity and got the airfare plus 3 nights at the holiday inn city center downtown chicago for 440. this was 3 days before i had to leave, so great deals can happen at the last minute.
You may also want to consider flying "stand-by" If you are flying on a major airline, except southwest and a few other super discount carriers, then you can buy the cheapest flight which is usually the last flights of the day. then you come to the airport earlier in the day and "stand-by" for the flight you want. this is good for single travelers. I would not recommend doing this if your traveling with others as you can be in for a big upset, especially if you want to sit near on another. Worst case you don't get the flight you want, you can still fly on your original ticket. i do this all the time and i have never had to take my original flight.