in a economic downturn what can happen in countries that depend on high taxes to fund social programs

If those taxes come from the wealthy individuals or from large corporations the latter will eventually oppose and resist such taxes under the pretext of the economic downturn.

The government will have to decide whether they resist such actions or reduce the taxes for the wealthy and increase public debt. The government also might try to apply austerity measures (reduction of public social protection and assistance programs as social security, food stamps, etc.) to compensate for the loss of tax revenue.