I have to say that I'm surprised by the outpouring of negativity and horrified replies urging you to trim down your itinerary. It's true that what you propose in your first posting will be a bit frenetic, but not everyone likes to travel the same way, and for some people (me included), whirlwinds can be fun and adventurous - especially if you just want to get a taste. No, you won't have time to explore each city to its fullest and you might feel a little dazed, but you'll also feel exhilarating.
My story is a case in point. In 2007 we went to Dublin, Dingle, Kinsale, Edinburgh, the Highlands, York, Bath, London, Amsterdam, Haarlem, Edam, Brussels, Paris, Versailles, Venice, Ljubljana, Bled, Postojna and Vienna. Insane, right? Well, it was - but we always wanted to spend a month backpacking across Europe and so that's what we did. We had one month to kill before living in Poland, and we made the most of it.
For three of us riding trains and taking a few Ryanair flights, staying in everything from B&Bs to hostels to nice hotels, we spent $12000 for 28 days. That's about $4000 per person for more time than you are planning on travelling. The exchange rate was approximately the same at the time - unfavorable.
A couple words of advice on your itinerary. You could fly into Dublin and make your way down to Paris, then take the train over to Germany, Warsaw and Copenhagen, and then fly to one of the Italian cities before finishing up via train....
It's one thing if you decide that you really don't want to rush, but if you truly want to see as many cities as possible, don't feel like it's not a worthy trip. It really all depends on your own travelling style and how much endurance you have. I could travel like this; some of my friends and family would keel over and die!