In my opinion, your heavy background in C++ will only yield you more respect and more serious attitude in the eyes of good employers. There was somewhere an article on JoelOnSoftware about how bad it is that students are now taught Java instead of a low-level C++ so that they have no good understanding of what is happening behind the scenes.
It is like a swim moving to C# after C++ since you (supposedly) already know how to design software and will avoid traps built by a high-level language.
Can recommend this book. I myself learnt C#/.NET after years of C++ with it.
C# and the .NET Platform, Second Edition
And - yes - I just dropped one job then had a break for six months while reading the book at the time. This gap is marked in my CV just for what it is - "Migration from system to applied development, mastering .NET/C#" or something like that.
Read it for a couple of months, try doing some simple projects, maybe not installable but web application if you'd like to get into it, then try applying for a job.
Anyone can learn Java or C#, but not everyone will be able to write quality applications in them.