These countries also typically have the largest budget deficits. So there is no scope to stimulate demand via fiscal policy. This would be in conflict with the requirements of the Stability and Growth Pact, and would entail even larger structural budget deficits.
When the economy was stronger, these euro member states failed to improve the underlying fiscal position, and in several countries it was even weakened. Therefore we now face a situation with large structural budget deficits, and have forfeited the flexibility which the Stability and Growth Pact is intended to give.