It's a difficult thing to gauge, because the answer is really dependent upon numerous factors, as you already pointed out.
1) the aptitude and flexibility of the developers in question
2) the difficulty of the project being undertaken
3) the management ability of the program managers (which is already in question, considering that they're hiring Java programmers to do .NET work)
With regards to point #1 --
I work in a corporation that has an IT department of Java developers, another one of Coldfusion developers and another one of .NET developers. In my experience, dyed-in-the-wool Java programmers don't like to switch sides - they see it as some betrayal of their innermost values. However, if you're fortunate to find a developer that realizes both sides of the fence (being Java and .NET) have a lot to offer, then you're off to a very good start! But if you end up with a developer who is convinced that MS doesn't know their way around the block still, then you're likely to have a sub-par performance. Again, it comes down to individual aptitude and flexibility.
However, if I had to give a time estimate on how long I think it'd take a really good Java developer to pick up .NET then I'd say you shouldn't be looking at more than a week's time (assuming that you put in 40 hour weeks), and two weeks at most.
Also, Java developers going to C# seem to pick it up much quicker than Java developers going to VB... I think it has to do with the difference in syntax (ie - C# is much more similar to Java then VB is).
Don't forget that you're also going to need to allow time for setting up developer boxes that have .NET installed (patching them and whatever else), but .NET installs are pretty slick now and it shouldn't take but maybe a day for this.