Maybe the first thing you think when you read, “Abolish the Senate,” is that this would be a radical change away from the government envisioned in the Constitution. Of course it would be a big change. But I think there's a more central and important Constitutional value that would be served by getting rid of it: the legislature makes the laws.
Ever notice how when the White House changes hands the strongest policy voices on the winning side of the aisle in Congress start looking for executive-branch positions? With the houses of Congress often set against each other it's hard for them to have any impact there. In charge of more unified executive agencies they can take the lead on policy and then, when they have to, get the issues they want before Congress. The people that stick around in Congress are the ones that specialize in whipping votes and using parlaimentary procedure for partisan advantage.
It's not only in line with Constitutional ideals that Congress should lead on policy, it would have good results. Congress holds a larger and fuller ideological gamut than any Presidential administration. We could get a wider range of ideas from there. An empowered and revitalized Congress might have a wider range of parties if alignment with Presidential politics wasn't so critical. We could see a broader range of compromises crafted to unite various factions that exist within and between parties. But we'd also get more stability. The makeup of Congress, even after a big swing election, doesn't change as much as the makeup of executive agencies after a Presidential election. Because it's made up of many little elections it represents all the people and interests in a fairly stable way.
So that's the body that should lead on policy: a strong Congress with one house. That means we need to get rid of a house. If we remove one of Congress' houses it should be the Senate. The one that's extremely unrepresentative and, honestly, truly obnoxious in its self-importance. I'm not going to go on about this — if you're not with me here you're not going to be with me on any of this :-).
One thing people seem to like about the Senate is that it gives a voice to concerns that would be drowned out in a representative body, where big cities would dominate. If we have a group that does this its powers should be more limited such that it doesn't blunt the legislative thrust of Congress too much. And it probably shouldn't be organized by state — really the power in the idea would be to raise up groups that cut across that relatively arbitrary geography. Maybe some seats could be reserved for proportional representation by party (as in many parlaiments), possibly with a formula that limits the number for the largest parties (which would be well represented in the more powerful House) to raise up smaller ones. Of course the smaller parties would have to get a bit more serious than they are today but they might rise to the challenge. Agricultural interests, which get strong but uneven representation in today's Senate, could be considered in a more balanced way. In any such body recognized tribes should certainly have seats, and so should any territory that isn't fully represented in Congress today. Maybe non-citizen residents could get some seats? Other racial and language groups might be worth considering, though the details would be hard to hammer out.
But the details aren't the most important thing. This isn't going to happen soon, and if it does eventually, I'm not going to lead it. Just trying to get all five of you that read this to think about the Senate. Its form and its power are written into the Constitution, but it might be eroding Constitutional values (at least the ones we value today). We should give a serious thought to abolishing it, to promote those values.
POSTSCRIPT: I tried to write this in a way that's neutral on current politics but it would be dishonest to ignore that abolishing the Senate and empowering the House would benefit my politics in the short-term. I think it's reasonable to believe this would be the case long-term. But my own politics aren't all I care about. It's very reasonable to disagree with my politics on many points, as well as my point of view on the Senate. I probably leaned harder into “Constitution Equals Good” thinking here than I really believe, but... hey, I'm American, I'm stuck with the rhetoric like all of us are. Oh, yeah, and anyone that actually knows about this stuff will clearly see that I don't. Because of that I tried to keep it short and sort of failed. Oh, well. At least I mostly stayed focused. There are many American political institutions that are bad and should be replaced with better ones for the good of democracy; this post is about one of them :-).