House blower motor runs when thermo is on Heat/Auto, but relay just clicks repeatedly when set to A/C or On?

If I turn the heat on, the fan runs normally. But if I turn on the A/C or set the thermostat to the 'On' position, the relay clicks over and over, and the fan never fully starts. In A/C mode, the outside unit starts, but the inside fan doesn't. The relay clicks, and the fan tries to start, but never fully starts. Bad relay? Bad thermostat?