I think the only reason one would suggest abolishing the senate is because senators are bought by special interest groups. I don't think the solution, if one believes that, is to abolish the senate. The senate is part of the carefully constructed system of checks and balances in the US constitution. Senators have different responsibilities that those of the House of Representatives, and each state gets an equal number of senators but there are far fewer of them than Representatives. All of these features are carefully designed to balance the executive and judicial branches.
The Senate serves a very important function in the structure of government; without it, there would be an imbalance of power--the antithesis of what the Founders intended. The only way it could be abolished is if something similar took its place, which would, of course, defeat the purpose of getting rid of it in the first place. I'm curious what prompted such a question.
Of course we should not abolish the Senate, in my opinion. I think that having a bicameral legislature is a very important part of our system of government and abolishing the Senate would be a grave mistake.
In our system, we try to make it hard for the government to act rashly, on the spur of the moment. Because of this, we have the Senate whose members are not elected all at once (one third of them every two years).
Let's look at the potential "Tea Party" victories this year. Let's imagine that the Senate was gone and only the House was up for reelection. Many Tea Party candidates could win and make major changes. This might be good or it might be bad, but it would certainly be hasty.
Instead, with the Senate, the Tea Party can't get a majority (or anywhere near it) this year. It will have to continue to be strong for at least another couple of years to get much power. If it does, so be it -- it means that Americans really believe in it. But we at least need the Senate to make us think for a while before diving in to major changes.