Yes...but maybe not in the way you are thinking. I think most will be able to match (though some don't...at least the first time around). The real problem occurs during post-doc and in the job market. For every Mayo or Hopkins position, there are hundreds of other positions that will be okay with "good enough"....as long as they can pay that person less money. The top & bottom 10%'s probably won't be effected, but everyone else in the middle will get squeezed.
There is probably a bell curve of sorts that represents the total # of applicants that apply to a job, in relation to how sought after the position may be....for whatever reason. In California and NY, I've seen positions posts for $50k/yr.....AND you have to find a way to afford housing in NYC, LA, SF, etc. People will line up to apply for those jobs because they value location over a fair wage. If there weren't 50-100+ applicants trying to land the job, then the person receiving the job offer may actually be able to negotiate a better wage. Add on top of all of this the pressure from mid-levels...and you have quite a mess.