Paying off the National Debt certainly didn't cause it. Cutting taxes almost continually helped, but I would never say it was the only cause. It was a group of things, not just one thing. It was far more complicated than cutting and raising taxes.
All markets were generally bad. Coolidge paid no attention to farmers who couldn't afford to raise crops, or industry workers who couldn't afford to keep the family going. When the European market collapsed (Mostly because of WWI debts) the US suddenly lost its form of income through exportation and importation. Coolidge was a provincial man in outlook, and a simple man, and a lucky man. He was out just before our market collapsed, leaving Hoover with little warning, and little chance of political survival.
The US lost the european market due to retaliations on Smooth-Hawley, not because of any european market crash. That is a myth propagated by leftists.