Should budget cuts even be on the table when there is such a high unemployment rate?

This is, sadly, a matter of opinion.  Macroeconomics is a
relatively uncertain field of study and we cannot know for sure what impacts something
like budget cuts will have on the macroeconomy.

Some people
argue that we should not be cutting the budget when we have a high unemployment rate. 
This case is made by Nobel laureate Paul Krugman in the New York Times link below.  He
argues that cutting the budget will lead to further job loss.  This will happen because,
for example, the money in the budget was being used to pay government workers who will,
instead, be laid off.

However, there are those who argue
that budget cuts will actually cause economic growth.  They argue that budget cuts will
reduce the deficit and will cause people to be more optimistic that the government is
acting effectively.  As people become more optimistic about the future, consumers will
spend more and businesses will invest more money and hire more people.  In this view,
the budget cuts will restore confidence in the government and the
economy.

Sadly, there is no way for us to know for sure
which of these will happen.  Therefore, we cannot actually know if budget cuts should be
on the table at this time.