Perhaps you stand a chance, if you either (a) are in complete control of your Party's senatorial nomination process, or (b) you live in a sparsely-populated State. But even then, look at South Dakota's perpetual reëlection of Tom Daschle.
It's not because people have bought into any "myth"—it is a direct result of the fact that you literally have better odds of winning the lottery (in a populous State) than you do in effecting the outcome of the Senatorial election.
The Senate was never intended to be popularly-elected. With a populace as utterly ignorant of the principles which make up our Government, I completely understand now, exactly why that is...
Suffice it to say, you and I will never see eye-to-eye on that subject.
However, your reference to Daschle relates to my broader point.
Namely, that the people's will is more powerful than any other force in American politics.
South Dakotans kept reelecting Tom Daschle precisely because they believed that he represented their interests in Washington D.C., in spite of philosophical differences.
Once it was brought to their attention just how little he and they had in common-and how ineffective he was in helping their state from a nonpartisan perspective-they defeated him.
However, all of the expensive ad buys, and RNC phone banks would not have made the slightest bit of difference if the people of South Dakota felt that he should be elected to a fourth term in office.
Yes, it's almost impossible to defeat incumbent senators, but what makes it even more difficult is the apathetic attitude that so many Americans take to politics.
McCain-Feingold, a.k.a. The Incumbent Protection Act, has made it even more difficult.
However, in some ways that anti-Constitutional desecration was an illustration of how weak that legislative chamber really is.
It showed us how petrified our purported voices in Washington our of their constituents.
If we can harness that fear for our advantage-in order to enact real change-then I guarantee you that this atmosphere of alienation and apathy will start to change.