Chief executive officer Travis Tygart said Armstrong was granted a two-week extension to Wednesday's deadline to tell the USADA whether he will help or not.
Netanyahu recently asked Israeli President Shimon Peres for a two-week extension to build the coalition, putting his new deadline just ahead of Obama's expected arrival in Israel.
Chester have won just twice in 23 matches since Christmas Day - and have picked up just four points from nine games under Davies, who was handed a two-year contract extension earlier this week.