It depends on how high the taxes are. If the taxes are raised to 90%, yes, absolutely that'll slow the economy to a halt. If the taxes are raised up to 5%, on anyone who earns $250,000 ***NET*** per year (net = final number after all deductions and before taxes). 5% on $250,000. That's $12,500. It's nothing to them.
It sounds good, just an additional 5% tax! Who could object? But the fact is higher taxes stifle job creation, always.
Here is a very helpful equation: GDP = C + I + G + net exports
The I in the equation is investments. That is what produces the tools and businesses that make “stuff” and buy and sell services. Increasing government spending, G, does not increase productivity. It transfers taxes taken from one sector of the economy and to another, with a cost of transfer, of course. While the people who get the transfer payments and services certainly feel better off, those who pay taxes are left with less to invest in private businesses that actually increase productivity. Over the last two decades, the net new jobs in the US have come from business start-ups. Not large businesses (they are a net drag) and not even small businesses. Understand, some of those start-ups became Google and Apple, etc.; but many just become good small businesses, hiring 5-10-50-100 people. But the cumulative effect is growth in productivity and the economy.
If you take an additional $12,500 in taxes from a small business that nets $250K a year- you take that money away from investment and that means fewer jobs.