Here are two games with 4...Nxb4:
@ NotKasparov: You gave the answer yourself: 4...Nxb4 is playable, but gets to the same position as 4...Bxb4 5.c3 Bc5, which highlights its main drawback: a certain lack of flexibility. After 4...Nxb4 5.c3 there doesn't appear to be a sensible alternative to 5...Nc6, whilst after 4...Bxb4 5.c3 White has to expect 5...Be7 or 5...Ba5, too, in addition to 5...Bc5.
Why not 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4 Nxb4 5.c3 d5; if 6.cxb4, then 6...Bxf2+ 7.Kxf2 dxc4 and black has two pawns for a piece and has weakened the white kingside. Might be good for blitz.
Why not 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4 Nxb4 5.c3 d5; if 6.cxb4, then 6...Bxf2+ 7.Kxf2 dxc4 and black has two pawns for a piece and has weakened the white kingside. Might be good for blitz.
For blitz, maybe. Anything else is out of the question. The only thing white might have to worry about in that position is the queen coming to d3 but Qe2 should drive it out, and white's king should be fine.
In the Evans Gambit (1. e4 e5; 2. Nf3 Nc6; 3. Bc4 Bc5; 4. b4), is 4. ...Nxb4 a viable option for Black? I've looked in a few opening books and a few online sources, and the possibility is not discussed. White might be tempted to take the e5 pawn, but after 5. Nxe5 Qf6 the undefended Knight is pinned to the Rook and the Queen threatens immediate checkmate with 6. ...Qxf2++. If 5. c3, then 5. ...Nc6; 6. d4 and the position is just like the common Evans Gambit variant 1. e4 e5; 2. Nf3 Nc6; 3. Bc4 Bc5; 4. b4 Bxb4; 5. c3 Bc5.