I've seen nothing to indicate it won't...academia is traditionally somewhat sheltered from the economy, since oftentimes people go back to school when the job market gets tough. Any funding that relies on tuition money isn't going to take nearly the hit that other industries have. Grants are certainly tougher right now, but the stimulus package may help with this and again, its "tougher" but its nowhere near the train wreck the financial industry is in right now. The other major placement type is clinical work...frequently at hospitals, which again, tend to be somewhat sheltered relative to other industries.
What you might see is a cut in the number of slots that are open, maybe a few programs that were on the edge to begin with dropping their funding, but I'd be surprised to see a large scale movement away from funding grad students. Any school that does so is probably going to struggle to find qualified applicants who are willing to go there. There's plenty of belt tightening going on for sure, but I haven't seen so much as a hint that fully funded programs will cease to exist anytime in the near future. Competition might increase in the short term if schools cut spots, but I think its far more likely that schools will reduce their slots than not offer funding.