The Chicago-based First District Appellate Court issued its order Monday.
Supporters gathered signatures to put a measure on the ballot to limit legislators to eight years. But a lawyer for top Democrats sued, and a judge ruled last month the measure didn't meet constitutional requirements to be on the ballot.
The Illinois Supreme Court said last week it wouldn't hear an immediate appeal. Supporters then asked the appeals court for an expedited process, because state election officials must approve the ballot by Aug. 22.
Republican Bruce Rauner is leading the effort. He's made it a major issue in his race against Gov. Pat Quinn.