Fiscal policy is supposed to be used to prevent economic instability. However, if used improperly it can well lead to instability.
Fiscal policy is supposed to be used to manipulate levels of aggregate demand to keep an economy growing that the proper rate. When an economy is not growing quickly enough, taxes are supposed to be lowered and spending increased. When an economy is overheating, the reverse is true. In these cases, fiscal policy would bring about economic stability.
However, there are times when fiscal policy is used unwisely. Politicians typically are willing to continue to increase spending and cut taxes even at times when there is no need to stimulate the economy. This could lead to excessive inflation. In the US today, there is a threat of economic instability because taxes have been cut and spending increased to the point that the country faces a huge deficit and debt problem. The fact that Congress cannot agree with the President on how to fix the problem adds to the potential for economic instability.
In general, then, fiscal policy can cause economic instability when the wrong fiscal policy is used at the wrong time.