County residents want an ambulance to arrive when they need it, and medical first responders want to show up for the call. But that connection, between victims and rescuers, has been threatened by budget problems neither group caused nor controls. As Allegany County officials call for a $2 million cut to emergency medical services, the union that represents 46 full-time Department of Emergency Services employees has tentatively agreed to some terms, and awaits proposed amendments to its contract from the county.