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And we'll just have to see how seriously they'll take it...
Anyway, the press release is here, but the most relevant part is:
All 2012 U.S. Open Cup matches until the final are scheduled for Tuesdays, with the championship taking place on either Tuesday, Aug. 7, or Wednesday, Aug. 8. In the first round, 32 amateur-level sides will be paired geographically, with the restriction that teams from the same qualifying pool (meaning USASA regional qualifiers, PDL and NPSL) cannot be paired. The first-round winners will face Division II or Division III clubs in the second round based on geographic proximity. Second-round winners play Division I clubs in the third round, matched on a geographic basis.
Emphasis mine. Read "Division I" as MLS clubs.
The third round starts on May 29. The remaining dates are June 5 (fourth round), June 29 (quarters), July 10 (semis) and the aforementioned finals on Aug. 7 or Aug. 8. June 29 is a Friday, all the rest of the dates are Tuesdays.
The only real scheduling congestion would come during the quarters and the semis, with a trip to Toronto FC the day after the quarterfinals and a trip up to Foxborough, Mass. to visit the New England Revolution two days before the semi-finals.
There are no dates for the Audi Cup yet, and it still remains to be seen if the Red Bulls get an invite anyway, but it might be something to keep an eye on.