1. I suspect that as Secretary of the Treasury it is unlikely he’ll have any emergencies that require working on Shabbos, unlike his current position as the President’s Chief of Staff which deals with true emergencies. I wouldn’t be surprised if this affected his willingness to accept
whatg is probably a “fool’s errand” since the budget situation is probably hopeless given the realities of partisan politics.
2. His frumkeit isn’t an issue. His economic policies are what many frum Republicans object to (though in all fairness, most frum jobs support “tax and spend” policies – just look at the press releases in YWN celebrating increased “pork” obtained for the frum community).