Regardless of the quality of the program, some students turn down their GTA and GRA offers. This means that if you are persistent enough you might be able to get an offer in the second round. This is particularly true if you are a U.S. citizen. To be considered for the second round, talk to the person responsible for making the appointments. Do not be afraid to call.
Persistence pays off.
Just do it. Better yet, make a trip to the department and talk to the responsible people in person. Explore both GTA and GRA positions. The tactics used to get each are slightly different. The GTA positions are usually controlled by the department and are offered to students to support the department's undergraduate teaching program.