I would suggest the agencies simply refuse to comply with whatever court order comes down and instruct all local and state police to cease providing aide or support of any kind to the Feds. Let Obama send in the Army.
The Utah state officials have been complying up to this point, hoping for the appeals process to eventually overturn this foolish decision and order.
Unfortunately, Obama would have legal authority and precedent on his side (something he doesn't always have) if he were to send in the Army, based on the court-ordered school desegregation cases in the South during the 1950s and 1960s. (Whether or not the Army would cooperate is another matter.) The Utah AG is undoubtedly aware of this and is trying to avoid a physical confrontation.