A interesting question.
Because some governors might not accept the money, Congress added a unique provision, in subsection 1607(b): "If funds provided to any State in any division of this Act are not accepted for use by the Governor, then acceptance by the State legislature, by means of the adoption of a concurrent resolution, shall be sufficient to provide funding to such State."
If state law does not give the state legislature the right to bypass the governor, how can Congress just change that law? Where does Congress get the power to change a state constitution?
It might appear quaint to note that the U.S. Constitution does not create a central government of unlimited powers. Congress only has those powers that the Constitution gives it either expressly or by implication. That's a lot of power, to be sure, but it's not unlimited.
The two main sources of power that might justify subsection (b) are Congress' power over interstate commerce and its power to tax and spend. The commerce power does not support this law. The commerce power is very broad indeed, but there are limits. One important one is that Congress can only use the commerce power to subject the states to "generally applicable" law. For example, if Congress sets the minimum wage at $7 an hour for all workers in interstate commerce, that law can include state workers in interstate commerce. But subsection (b) is not "generally applicable." By its very nature it only governs states.
The second main source of federal power is the spending power, allowing Congress to bribe the states to take certain actions. For example, years ago Congress told states that it would reduce federal highway funds to any state that did not increase its legal drinking age to 21. The court upheld that law, with Justices William Brennan and Sandra Day O'Connor dissenting.
The spending clause does not work here. Congress is not telling a state, "You must change your state constitution before we will give you a dime." Instead, Congress is simply telling the state, "We have changed your state constitution so that we give more power to the state legislature, without any pesky interference from the governor."
It is unlikely that subsection (b) will survive constitutional challenge. Does that mean that the entire law is unconstitutional or only subsection (b)? That depends on whether Congress considered the entire bill to be a uniform whole, so that if one part must fall, all must fall. Or, did it want the courts to sever the unconstitutional part of the law and leave the remainder intact?
It may seem silly to worry about such matters when we know that Congress was in such a hurry to enact this bill that a great many congressmen—perhaps all of them—did not have a chance to read all of it. But, the courts will still have to decide the severability issue and invalidate more than subsection (b).
Some people incorrectly think that "state's rights" is an anachronism. The purpose of state's rights is not to protect the "states" from the federal government; it is to protect us from the federal government. As Justice Hugo Black reminded us over 40 years ago, "The proceedings of the original Constitutional Convention show beyond all doubt that" the framers denied Congress "the power to veto or negat[e] state laws," but that is exactly what subsection (b) does. To give Congress such power "distorts our constitutional structure of government." But that is what subsection (b) does.