1) You are missing a last double quote on the end
2) Are DT and Press variables or constants? If they are constants, then you don't need to add them using concatenates.
strSQL = "SELECT * FROM tbl_jobs WHERE accounthandler='DT' AND type='Press' AND printdate>='" & firstdate & "' AND printdate<='" & lastdate & "'"
objRS.Open strSQL, objconn