Popular misconception in Europe that you need 3000+ hours to get a job with any airline in the US. Fact is until recently (last tuesday) to get a job with a commuter like flying an emb-145 at COEX you had a look in with 800 TT and 200 Multi. In fact this has been quite standard for them over the past 12 months. At the other end of the commuter scale is ACA that has been looking for 1200TT and 400 Multi for the CRJ.
As far as Majors are concerned, yes, you'll need around 4000-5000 TT and a bunch of P1/PIC time.
Of course, last tuesday changed that, and right now everyone is cancelling class dates and interviews for the rest of the year. Probably longer.