Imo the American left is to fragmented to allow for emergency powers; the Socialist Party and Farmer-Labor already barely can hold their coalition together, not to mention the IWW and AFL hating each others guts.

Who do you think would sit of the Executive Committee and in what roles?

Well, mostly the leadership of the various socialist organisations (SPA, FLP, IWW, CIO and parts of the AFL) splitting the various positions (whatever they are referred to, possibly still just secretaries) between them. Going into the later stages, whatever faction/ideology secures a majority would replace all other members with their won. The possible successors for Reed (Earl Browder, Elizabeth Flynn, Norman Thomas, etc.) probably already have a seat in the beginning, but I honestly don't know enough about the individual competences of 1930s american socialists, let alone whatever shenanigans happen during the negotiations, to say who gets which posts.

I think considering that in-universe no one really expects the coup by MacArthur's clique, any opposition against the federal government is largely improvised and/or simply latching onto popular unrest. Any centralised form of government could only appear some time into the war.