Does the US Govt. get more tax revenue when they cut taxes because people are making more money?

Answer 1

In theory, they get the same percentage of taxes. With lower taxes, people are more apt to spend and give an illusion that things are worth more. Hence, the government can receive more taxes.

They use the same principal when they want to tax more. They say that people are spending more and they have the extra income so they can tax more.

Answer 2

In part. Cutting taxes also reduces the encentives to engage in tax avoidance and tax evasion. It can also simply be because there are more people working (job growth) or just more people (population growth - due to immigration, these days).