There are limits to this, some of which are set out in South Dakota v. Dole, 483 U.S. 203 (1987). These limits (quoting wikipedia) are:
* The spending must promote "the general welfare."
* The condition must be unambiguous.
* The condition should relate "to the federal interest in particular national projects or programs."
* The condition imposed on the states must not, in itself, be unconstitutional.
* The condition must not be coercive.
Especially the last condition is relevant. It means the withdrawal of funding cannot be so harsh as to be clearly funding. I believe the actual wording used is that the threat of withdrawal cannot be a 'gun to the head' of the states.
Reading through this comment thread is very interesting, I just can't help but try to understand how so many geeks are so well versed in case law :)
I don't even live in america, but the system is interesting and rather well represented in the media. Few countries are as attached to their constitution as the US.
This is actually a rather important principle, and most people don't realize how many federal laws that work at the state level use funding carrots rather than criminal-punishment sticks for enforcement. For instance, the penalty for not following the unpopular and eventually dismantled "No Child Left Behind Act" was that your state would not receive federal education funding.
> The Act required states to develop assessments in basic skills. To receive federal school funding, states had to give these assessments to all students at select grade levels.
https://en.wikipedia.org/wiki/No_Child_Left_Behind_Act