The big word in your post is "regular." Check out this page for examples of
some of the routes you have to choose from:

http://www.geocities.com/Pipeline/Dr.../bencross.html

If regular means once a year during the summer, and you don't mind waiting a
few days if the weather goes south, your longest leg can be as short as
500nm. This is just barely within the range of a 172 with 50-gal tanks, just
to make the point. Something like an A36 or light twin would probably handle
this pretty well, perhaps unmodified.

But, if you want to be able to make the trip regularly, and without tons of
weather delays, you're going to need a lot more range, and things go
downhill very quickly as you need to carry more gas and you need a bigger
airplane to carry all that gas and the bigger airplane needs a bigger engine
which burns more gas to carry all of that gas which now by the way you need
more of...

The more relevant question is why would you want to, even if you could? The
airlines will gladly take you on the same trip in much less time and with
much higher safety, and feed you champagne and strawberries on the way. And
their dispatch reliability will put yours to shame.

I'd love to do the trip once, just for the sake of doing it, but this is one
of those few cases where the numbers really favor the airlines, even if you
have money to burn.

-cwk.