When the US Senate was first created it was a body of persons (well, originally only men, but we know a woman can do just as well if not better than most men) to be selected in a manner preferred by the state legislatures. The Senate was a body that was not only a check on the President, the House of Representatives, and the Supreme Court, but was also a check on the federal government making decisions without proper input from the state legislative bodies. Granted, some legislatures decided to have state wide elections for their senators, but many if not most of them selected the senators themselves. This bicameral structure with one house is directly elected by the people and actually has more representatives in it (here known as the US House of Representatives) and having another house with different responsibilities being unelected comes from the British model with their House of Commons and the House of Lords. This structure still exists there to this day, with the House of Lords' power being severely limited by the lower house (note that our Constitution does not call one upper and the other lower, but people still consider the Senate the upper). The difference in the Lords and the Senate is that the senators were selected by democratically elected bodies. Having this structure has someone in the federal government looking out for the interests of the state governments. Now, too much state government independence on the federal level is a counterproductive thing (see Civil War), but imagine the different dynamics in the federal government if this were the case. If there was someone representing a state government saying that they do not have enough resources to carry out a federally mandated but not funded initiative, that they need more money for school programs, that a federal law crosses the line of a historically state-held responsibility. State governments are very important entities, but seem to fall in the backdrop when compared to the federal government. There is also another issue that could be raised about the diversity of people that may end up in the senate. Perhaps state legislatures would choose people who are well known and accomplished in a particular field of (science, academics, law enforcement, government, economics, community organizing, health care, the list goes on and on...) in order to have experts not only testifying in Congress, but actually being a part of the legislative body.
I understand that the issue of state level corruption comes up when thinking about this, but think about how many people you know that actually trust their elected officials. Direct democracy does not prevent corruption at all. At least if we have government officials that are answerable to bodies that have the resources to investigate them and keep a close eye on their actions in office, perhaps we will see more consistency in their voting record, less campaign contribution corruption (likely there would not be many campaign costs), and someone who is answerable to a committee that can sit down and thoroughly go through their record, holding them to greater accountability. Perhaps more members would show up to committee meetings, perhaps more members would take an active part in floor debate, perhaps more members would think very carefully about the legislation before just jumping right in.
I can understand the apprehension to this idea. It takes the power out of the hands of the people, it is bad for democracy, and democracy is what we are all about. True, it does take power of selecting senators from the direct hands of the people, and this is a limit of direct democracy. However, unchecked democracy is a very questionable thing. The founders knew that, and our current political situation reflects this. Our democracy is placed within some parameters by our federal and state constitutions. Many see them as granting democracy, but they place guidelines on how our democracy is expressed to prevent all decisions from being made by large groups of people working on an emotional high, not reasonable thought. Our US Supreme Court is also a limit on democracy. The justices are selected and approved by elected officials, but after that are free to interpret the law as it is written (which is a product of representative democracy) without worry of public opinion, which should not figure into their deliberations. We do not ask of any other judge that they take a public opinion poll before ruling in a case, and this should surely not be the case here.
This is a situation for consideration. Think about how it may be different if the Senate is what it was supposed to be originally. Perhaps it would have evolved differently. It may become a "chamber of sober second thought" like the Canadian Senate, where larger bills go to be dissected and carefully debated. Perhaps their authority to reject certain bills would be more limited, thus making the chamber less politically powerful, but still influential, and certainly maintaining its media power (which is just as good if not better than actual power granted by constitution and law these days). I would not mind a Senate that was representative of my state, not just the voters, but the entities of my state as well. Just a thought.