With filibuster reform bubbling its way up the agenda (since, let's face it, the next Republican Senate will effectively eliminate the filibuster no matter what), I thought I'd look at the question of whether current Senate dysfunction is driven by the increasing population gap between small states and large states. I took a weighted sum of the population of the largest 10% of states, and compared it to the same figure for the smallest 10% of states. For example, there were 13 states during the initial 1790 Census. So I took 100% of the population of the largest state and added it to 30% of the population of the second-largest state. Then I did the same with the two smallest states, and divided the first number by the second. If this ratio goes up, it means that the large states are growing faster than the smaller states, and that the large states' underrepresentation is getting worse.
When the colonies ratified the Constitution, Virginia and Pennsylvania had roughly twelve times the population of Delaware and Rhode Island. The large states continued to grow faster through the pre-Civil War era. Most of this growth occurred in the Northeast and Midwest. During post-Civil War reconstruction, Republicans aggressively granted statehood to prairie and mountain west states to expand their political coalition, causing the ratio to spike in 1890 with the addition of North Dakota, South Dakota, Montana, Idaho, and Wyoming. In the second half of the 20th century, three major events reshuffle. The addition of Alaska and Hawaii to the Union; modern air conditioning making the Sun Belt a more attractive place to live; and the decline of industrial employment in the Northeast and Midwest. Today, the large states are more underrepresented than they have been at any time in the country's history, except moments where new (usually small) states were added to the union. But the large states aren't that much more underrepresented than they were in, say, 1950.
Let's look at a slightly different number, the percentage of the U.S. population living in those large states.
This paints a much clearer picture. The large states constitute a larger and larger share of the country's population. And the situation has gotten steadily worse since 1970. It's possible that by the end of the next decade, 40% of the country's population will be represented by 10% of the members of the U.S. Senate. That is not a recipe for political sustainability. But once again, current underrepresentation is only modestly worse than it was during much of the 20th century.
In conclusion, underrepresentation of large states is bad, and it's getting worse. But because it's not dramatically worse than it's been in recent times, it is hard to say that large-state underrepresentation is the root cause of the Senate's current dysfunction. Instead, we have to look to the fact that partisan alignment now mirrors ideological alignment (which was not true in the era of Dixiecrats and liberal Northeastern Republicans), and to the decay of Senate norms that prevented the minority party from using procedural gimmicks to obstruct the majority at each and every turn.