Asking if high taxes undermine the economy is akin to asking if I hit you with a baseball bat will it hurt. The answer is obviously yes, only the reasoning is different.
Love may make the world go round, but money greases the wheel and when the government grabs the grease the world grinds to a halt. It's the same with the economy.
For most of the twentieth century economic theory was based on the work of British economist John Maynard Keynes. Keynesian economic theory advocated an activist role for government in the economy. During hard times, Keynes advocated government pump money into the economy. During good times government would tighten up on the money supply. This led to swings in the economy as government always lagged behind the curve, over correcting after the situation had changed. One feature of Keynesian economics was high taxes. The government needs the money to control economic conditions. That caused two problems. Government timing was always wrong and the removal of capital from the economy caused it to operate inefficiently.
By the time of the Reagan Presidency, Keynesian economics had been superceded by the theories of Friedrich von Hayek and the Chicago school of economics. They produced the controversial "Laffer curve" that showed lowering taxes would actually provide more money for the government.
Reagan drastically cut the marginal tax rates and during his eight years in office federal revenue rose from 550-Billion dollars a year too nearly a Trillion dollars. Fulled by lower taxes the economy boomed and Washington received more taxes. Unfortunately, as they always do, Congress spent money faster than it came in so the national debt kept rising. Reagan's enemies blamed the debt increase on the tax cuts, but the figures proved them wrong.
Reagan was not the first president to learn lower taxes generated more revenue for Washington. When he took office in 1960, John F, Kennedy lowered the marginal tax rate from 90 percent and had the same experience as Reagan. Kennedy said it was the best thing he had done as President.
"Those who cannot remember the past are condemned to repeat it." George Santayana.
The Democratic party is still stuck in the Keynesian mode and so they are once again clamoring for higher taxes. That would be a disaster for an economy that is providing full employment and growing at a sustainable rate.