At Justia's Verdict, Vikram Amar (Illinois) has a three-part series on the independent state legislature theory — the first post is most relevant to originalism:
How ISL Proponents Deal With Arguments and Cases Cutting Against Them: Part Three in a Series
From the first post:
Another aspect [of the debate] is whether the “legislature,” however defined, can override state constitutional directives on how elections must be run. Remarkably, modern advocates of ISL offer nothing—nothing!—to suggest that anyone at the Founding would have understood state “legislature” to mean a free-floating body untethered to the state constitution. Or, a body whose legislative work-product would be free from state court jurisdiction and instead subject largely or wholly to federal judicial interpretation.
In fact, the meaning of state “legislature” was well accepted and bore a clear public understanding at the Founding: A state “legislature” was an entity created and constrained by its state constitution. The creation of new, republican state constitutions up and down the American continent was a truly transcendent achievement in the late 1770s, acclaimed and revered by Americans everywhere. These new state constitutions were the very heart and soul, legally, of the American revolution. These state constitutions were universally understood as creations of the American people themselves. So of course state constitutions were understood as supreme over state legislatures at the Founding! And of course state courts could—and did—enforce these state higher laws against state legislatures themselves. Notable state judicial review under state constitutions in fact predated the Philadelphia Convention and Marbury v. Madison.
Also, this seems like a good textual point:
In this regard, consider Article I, section 4, which vests backup power to regulate various aspects of congressional elections in “the Congress.” No sober person would think that this provision vests final substantive power in Congress to do things forbidden by other parts of the federal Constitution itself, a Constitution that indeed creates and bounds Congress. Imagine, for example, a congressional statute proclaiming John Smith by name as ineligible to run for Congress, in obvious violation of the spirit of the Article I, section 9 bans on federal bills of attainder. Or imagine a congressional statute proclaiming Catholics ineligible, in plain contravention on the Article VI ban on federal religious tests, to say nothing of the later First Amendment. No one would seriously suggest that federal courts lack power to interpret federal statutes regulating congressional elections with an eye towards harmonizing those statutes with constitutional rights. Nor would anyone deny that Congress has in fact deputized federal courts to perform these very functions.
All this is of course true for every provision of Article I that vests power in Congress. But the point is particularly sharp when we juxtapose “the Congress” and “the Legislature” of “each state” in Article I, section 4. If the federal Congress is quite obviously not independent of the federal Constitution, why should anyone think that the state legislature in this very same clause is somehow independent of its state constitution?
I have a lot more doubt about this later point though:
If, for all the reasons I have identified, the term “legislature” does not mean “independent legislature” but instead means “legislature as defined and limited by the state constitution,” why is the term “legislature” (rather than simply “state”) there at all? The most obvious explanation relates to efficiency and expense. The Framers knew that each of the thirteen then-existing states had an ordinary standing legislature, and Article II created a simple, inexpensive, and self-executing default that, unless a future state constitution specified otherwise by creating a special ad hoc legislative body or process, the state’s ordinary pre-existing state legislature would be the body to adopt federal election regulations.
I would say instead that the most obvious explanation for the Constitution's use of the term "legislature" is to give the power to the legislature and not to parts of the state government that are not the legislature (most notably the state executive and the state judiciary, the branches that under classical separation of powers theory are definitively distinct from the legislature). This conclusion isn't inconsistent with the idea that "legislature" means "legislature as defined and limited by the state constitution," but it retains some operative meaning for the Constitution's use of the word legislature. Thus, this point from the conclusion of the third post seems misconceived:
Instead, under the Tenth Amendment, each state is free to distribute power among different institutions within the state as it sees fit, subject only to specific federal constraints found elsewhere in the Constitution or federal statutes.
That's true, but it leads to the opposite conclusion from what the post contends: the state's distribution of power (in this case over elections) is subject to the specific federal constraint that the power must be exercised (as the Constitution expressly says) by the legislature.
Posted at 6:09 AM