In general, the most likely way for expansionary fiscal policy to destabilize an economy is for this fiscal policy to "overheat the economy." This would happen if expansionary fiscal policy is undertaken at a time when the economy is already expanding well enough on its own.
If an economy is at the classical range of the AS curve, expansionary fiscal policy will serve only to fuel inflation. This is true because the tax cuts or spending increases will move the AD curve to the right. In such a case, this policy could destabilize the economy by causing demand pull inflation.