How would a balanced budget amendment force government to enact a contractionary fiscal policy during a recession?Some politicians have suggested...

If a balanced budget amendment were passed, the government
would have to reduce spending every time tax revenues decreased.  The spending would
always have to be no greater than the revenues so lower revenues would mean lower
spending.

During a recession, tax revenues go down.  People
and companies make less money so there is less money to be taxed.  If there were a
balanced budget amendment, then, government spending would have to go down every time
there was a recession.

Reducing government spending is a
contractionary fiscal policy.  When the government spends less, fewer people are getting
paid (whether for work or via transfer payments like unemployment insurance) by the
government.  This means (all other things being equal) that unemployment goes up and
economic activity decreases.

In this way, a balanced budget
amendment would lead to less spending during a recession which is (to Keynesian
economists, at least) a contractionary fiscal policy.