Well, I echo many people here by saying 'great idea, but...'. To improve the economic situation, linking HS2 to Liverpool, a short tunnel to Prestatyn via Birkenhead, a new bridge over the Menai Strait and another tunnel from Holyhead to Dun Laoghaire might make a good start. That gets you to Dublin. Borrow a piece of either the Galway or the Sligo lines, then that shortens the distance still further. The nearest place you can reach on the other side is St John's in Newfoundland. It's about 1,900 miles (I don't know the exact distance). You then cross Newfoundland on the surface, a last section of tunnel to Cape Breton Island, bridge to Nova Scotia, call at Halifax, run down to Yarmouth, another bridge or tunnel to Portland and you're onto the US rail system. Link up the two stations in Boston, and I reckon you would be able to make the entire journey in less than 24 hours with about seven stops. It also links in with Via Rail at Halifax and ropes in Ireland, so adding the potential for additional funding.
The fact that I'm part Irish and have friends in Halifax has absolutely nothing to do with my ideas, of course.