The idea is not a merger of countries but a North Atlantic Economic Union. The problem is that one country, the US would have a majority of the economic activity, make it top heavy. One gets closer to the same place by the US and EU over time reducing trade barriers.
The idea of the dollar and the Euro currencies merging is interesting, but would force a common monetary policy, which might be unpopular as nations have different ideas as to how to balance employment, growth, inflation, interest rates, and the like.
I think a free trade agreement (an updated version of the Transatlantic Trade and Investment Partnership, perhaps) between the United States and the European Union, and a separate agreement with the United Kingdom, would be about the extent to which I support any kind of economic union.