One great way to have a cheap New Year's Eve party is to make it a potluck. Since the food will cost the most, everyone should bring a unique dish. Although most people will go out and buy something to bring anyway, it reduces the food cost to a bare minimum. The most you will have to supply are the cups, plates, and silverware which should cost $15 at the most from the dollar store. A nice centerpiece to have would be a glass bowl filled with sliced fruit or a punch bowl, or course "spiked" with your favorite alcohol to make things more fun but make sure everyone is above the age of 21.
Another great alternative to counting down would be to cut off the lights, and have everyone write a list of what they do not want to bring into the New Year. After they have done so, go outside and have a huge controlled fire to burn those. This should be very fun because when people have had alcohol and they see fire, it is likely that they will seeing a shooting star (or the illusion of one). The key to throwing a cheap New Year's eve party is to concentrate on your guests, the upcoming new year and the fun that you are having. After all, people will not remember the fancy food you had, they will remember how great of a time they had and how they felt bringing in the new year with precious loved ones.
A couple of things for a cheap new Years party is to have a potluck so food costs are minimized. You can also have play some fun games and some music playing. The music should be very easily accessible and free since everyone has some nice songs on their computer and if not you can download some. Then, at the time of countdown, you can have a bonfire which will top of the night. You can also buy some noisemakers and hats from party city from around a dollar each of the dollar aisle.
Since 2010 is the year of the tiger, you can ask that people dress as tigers which will enhance the mood and the environment. People are naturally creative so giving them some room to have fun and make something fun will make your cheap new Years party the most talked about of the New Year.