The first leg of your trip, Vancouver to New York in 2 months is doable, but you may not have time to explore. A quick initial search on Google Maps puts the route at a minimum of 4,800 kms. This would be the minimum, and on a bike I would realistically think that would be 5,500. I like to average 100 kms a day and take one day off every 5 days. My concern would be bad weather, mechanical issues, etc...that may push you to your time limit.

All that being said, I am sure it will be a great trip. Make sure you are comfortable on the bike that you are riding, and go have an adventure.