It's a simply answered question actually. First refer to the Laffer Curve.
Laffer curve - Wikipedia, the free encyclopedia
It's a wiki, but it makes the basics clear.
Taxes must find an equilibrium. A balance between income and burden that maximizes both the freedom of the people as well as cover the needs of the state. This is why we have a spending problem in this nation. The government has grown cancerous and bloated and needs to be cut back massively. Every power not given in the constitution should be cut back and given over to the states as is proper.
As for lower taxes, you decrease both the impetus and profitability of avoiding them and therefore increase revenues paid. This is also why simplifying a tax code is better because you cut away all sorts of ways for people to avoid taxes, save fleeing jurisdiction, which the wealthy can do if they feel that they are being unjustly or unfairly charged. There is so much precedent for this working it would take a dedicated fool to deny it.
Supply side works if you provide a beneficial place to invest and not to flee. Currently the economic environment here is poor at best, dangerous at worst. If you make it a good place for people to invest in this nation, and make it harder for them to do so off shore, money will return. That is the point of setting good economic policy and why Cal Coolidge said it best:
"The business of America, is Business."