Cadillac has had their share of problems with the "power module" which is a transistorized speed control device which takes the place of a blower resistor. I can't keep SeVilles and DeVilles straight, but one or both of those models and their GM counterparts use a blower motor which has an integrated power module.
Look under the hood on the passenger side firewall for the blower motor. If it has three wires going to it then you have this design which is a high failure item. Aside from the typical GM failures in power modules, the motor is positioned near engine heat and can cause quick death. Even though your description sounds like the power module is intermittantly opening, this failure can be caused by the motor drawing too much current. At any rate, the blower is an assembly so test it and replace it if necessary.
While the blower is currently inop, check that one wire has 12v, one wire is a solid ground (