No, I don't think the Governor sent him; Merle told him he killed Michonne, per his orders, but instead, she came back, killed his zombie daughter and took out his eye. The Gov is not the forgiving sort. He wanted Merle to pay by killing his own brother, which Merle also refused to do.
Merle is definitely on his shit list.
But Merle, for all his evilness, isn't a complete idiot. He's following his brother, for now and sizing things up. But I imagine he'll turn on the others, eventually--the only question is to what degree.