If it is just a numerical field, you should be able to do it similar to this:
query = " \"daily_YearMonthDay\" = 20131105 "
arcpy.Select_analysis(daily_stations, daily_stations_Select, query)
...or, in keeping your variable ref 'x':
x=20131105
query = " \"daily_YearMonthDay\" = {0} ".format(x)
arcpy.Select_analysis(daily_stations, daily_stations_Select, query)
This is native Python, see:http://docs.python.org/2/library/string.html