Fermilab may have better luck with supersymmetry. A few years ago, CDF discovered an event with two electrons and two photons, and a large amount of missing energy and momentum. The event was consistent with the production and decay of a pair of scalar electrons (a scalar electron is the supersymmetric partner to the electron). Still, there was a very remote chance that a known physics process could produce that event topology. If that were the case, they'd never see another one.
Deep rumor is that they've recently seen another one.
To claim discovery of Higgs, Fermilab needs to reach the blue band. To see any evidence of Higgs at all, they need to reach the green band. If you pick a Higgs mass along the bottom axis, you can read from the side axis how much integrated luminosity--how much data--they'll need.
According to the Run II schedule, Fermilab should receive 15 fb^-1 of data by the time LHC turns on in 2008. If that's the case, they'll be able to detect hints of the Higgs up to a mass of 180 GeV (about 180 times the proton mass), and claim discovery of any Higgs up to almost 120 GeV. But they are only on schedule to get about half of that, in which case they'll only be able to see hints of Higgs up to about 120 GeV, and won't be able to discover it at all. (Higgs has already been ruled out up to about 113 GeV.)
[Geek alert: The unit of data is called an "inverse femtobarn" (or fb^-1). A "barn" is a unit of cross-sectional area, 10^-24 square centimeters. A "femtobarn" is 10^-39 square centimeters. Because we measure event interactions by their effective cross-sectional size, it is convenient to measure integrated luminosity as an inverse cross section; then integrated luminosity times cross-section equals a number of events. So for a process with a cross section of 10^-39 square centimeters, you'd expect to see an average of one event per inverse femtobarn of data.]
New Scientist article on the last attempt to find the Higgs boson
An interesting Raytheon article putting it in perspective with regard to Cosmology