Several people have mentioned Article 1, Section 8. Here is what Thomas Jefferson has to say about that provision:1. They engage in political activities.
2. Their finances are not transparent.
3. There is nothing in the Constitution authorizing such funding.
Any other questions? Skippy
"To lay taxes to provide for the general welfare of the U.S." that is to say "to lay taxes for the purpose of providing for the general welfare." For the laying of taxes is the power and the general welfare the purpose for which the power is to be exercised. They are not to lay taxes ad libitum for any purpose they please; but only to pay the debts or provide for the welfare of the Union. In like manner they are not to do anything they please to provide for the general welfare, but only to lay taxes for that purpose. To consider the latter phrase, not as describing the purpose of the first, but as giving a distinct and independent power to do any act they please, which might be for the good of the Union, would render all the preceding and subsequent enumerations of power completely useless. It would reduce the whole instrument to a single phrase, that of instituting a Congress with power to do whatever would be for the good of the U.S. and as they would be the sole judges of the good or evil, it would be also a power to do whatever evil they pleased. It is an established rule of construction, where a phrase will bear either of two meanings, to give it that which will allow some meaning to the other parts of the instrument, and not that which would render all the others useless. Certainly no such universal power was meant to be given them. It was intended to lace them up straitly within the enumerated powers, and those without which, as means, these powers could not be be carried into effect." 15 Feb. 1791Papers 19:275--80
So, I will repeat, There is nothing in the Constitution authorizing such funding.