Kevin Flohe asks, “Do you think a unicameral legislature would be more or less effective at reining in executive power?”
Sorry, Kevin, but it’s a long answer. That’s why I moved it to the blog.
TL/DR version: At the margin, but the size of the effect would depend on the structure of that legislature.
I haven’t thought about that particular question before, but I’ve thought a lot about the growth in presidential power and Congress’s inability to rein it in. My answer is, at the margin, yes, but how effective would depend on the structure of that unicameral legislature.
The Framers envisioned Congress as one institution set up against another institution, the two of which could check each other effectively. What they did not seem to realize is that Congress is not one institution, not in any functionally coherent sense. Even more, it’s not simply two institutions, as we might think because it is bicameral.
In 1885, when Congress generally dominated the president, Woodrow Wilson wrote his doctoral thesis on how Congress did not provide good leadership because each member being responsible to a regionally limited set of voters, it could not focus on the national interest, only on a competing set of regional interests.
So what has changed to make presidents more powerful? Not the structure of Congress, but the system of selecting presidential nominees. Congress could dominate presidents back then because party leaders selected presidential nominees. Today the general public selects them, so party leaders, including Congressmembers, have lost that power over presidential hopefuls.
Not having that power over presidents, Congress would need to be more functionally coherent as one institution of government set against another in order to exercise effective constraints. But Congress has not become more coherent — regional interests still prevail over institutional interests.
Bicamerality is at best neutral in regards to the regional interests, but may make them marginally worse. The House is worst here, because House members are more likely to have a homogenous constituency they dare not buck.
Another important factor the Framers didn’t predict was the effect of party interest, which often works against controlling presidents, to the extent party members don’t want to harm their own party. This interacts with bicamerality, because while in any case one chamber may be desirous of checking the president and the other not, when there is divided party control of Congress bringing both chambers to bear against the president is even harder.
So now we can see what eliminating one chamber would do. It would eliminate the difficulty of needing to get two separate bodies to come to agreement on reining in a president, and how to do so. I suspect that’s what Kevin might have been thinking of. But it depends on party control. When the president’s party controls the single house of Congress, it would probably have no effect. But when the opposition party controls, the problem of the other chamber being controlled by the President’s party eager to protect their own is eliminated. So at the margin, situationally, this would likely help Congress rein in presidential power, at least more so than at present.
But just eliminating one chamber would not wholly relieve us of the regional interests that keep legislators from focusing on the national or their own institution’s interests, as envisioned by the Framers. Eliminating the House in favor of the Senate would have more effect than vice versa, but that is the less likely choice of chamber to keep if we shifted to unicameralism. So the size of the effect of unicameralism is dependent also on which chamber we keep, assuming we don’t change the remaining one.
If we change that one remaining chamber so that legislators are elected nationally — using a list proportional system, legislators would be less regionally beholden, and likely to be more able to focus on institutional interests and the national interest.
In summary, yes, a unicameral legislature ought to make reining in the president easier, at least at the margin, but the size of the effect depends on how much the legislators are distracted from collective interests by regional interests.
The Bawdy House Provisions 
Of course, there are plenty of options intermediate between nationwide list proportional of single member districts elected via winner-take-all. One could envision state delegations being elected by list proportional methods, or in very large states dividing the state up into a few districts, each electing 10 or so members, if one didn’t like the idea of super-massive districts with 50 representatives. The optimum choice here probably has as much to do with what people are comfortable with (ultimately, to whatever extent democracy can be considered legitimate, it depends on the governed buying into it) as with the technical merits of a particular district size.
As to list proportional, I geek out on the math of election methods (Arrow’s Theorem and all that), so at one time I was enamored of proportional methods that don’t involve lists. But they’re all either complicated (STV might work in practice, but I just don’t see Americans buying into anything with that many calculations) or inefficient at getting proportionality (cumulative voting is nice, but it requires coalitions to make good calculations about how many candidates to run). Letting people vote for a list and also one or a few candidates within that list is simple to implement, pretty efficient in practice, and hence probably good enough.
One way to rein in presidential power is for the president to be directly chosen (and when they so choose, removed) by congress. The senate can veto this decision by super-majority.
This doesn’t really speak to James’s point, but one of my suggestions for limiting presidential power is to give more power to the Senate to check the president. Under my plan, the Senate could veto executive orders and unseat cabinet officials for no confidence–all perhaps with a supermajority.
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