SMA PLT ON IFR APCH VECTORS DESCENDED THROUGH CLOUDS; HAD NMAC WITH SMA.

Narrative

ACFT DSNDING BDF-PLANO HDG 052 DEGS (SEE CHICAGO AREA) TO DPA. ATIS: 1100' OVCST; 5F-WIND 2815; LAND AND DEPART RWY 28.' OUT OF 4000' APCH TURNED US RIGHT TO 070 DEGS; LEFT TO 010 DEGS; 350; DSND (IN STEPS) TO 2600'. HE SAID HE COULD CLR US FOR THE VOR 28 CIRCLE TO LAND IMMEDIATELY; BUT THE ILS WOULD RESULT IN 'CONSIDERABLE DELAY.' WE TOOK THE VOR. HE VECTORED US NEARLY ON TOP OF DPA; THEN 'TURN LEFT TO 068 INBND; CLRNC FOR THE APCH. CONTACT TWR NOW!' ALL AT ONCE THE FOLLOWING OCCURRED: WE CALLED TWR; BROKE OUT AT ABOUT 1900' MSL (1100' AGL) AND WATCHED AN SMA PASS FROM 11 TO 5 O'CLOCK ABOUT 150 YDS AHEAD; 150' BELOW. WERE ONLY TERRIFIED FOR 2.65 SECS--LONG ENOUGH. TWR REPLIED; 'RPT FOX RIVER.' WE REPLIED; 'WELL PAST FOX RIVER ON DEP END OF ACTIVE 1900'.' CTLR TURNED US RIGHT TO LEFT DOWNWIND. NO FURTHER PROBS. NO ONE COMPLAINED. I DOUBT ANYONE ELSE RECOGNIZED ANYTHING WAS WRONG; BUT WE DO. HOW DO WE PREVENT THIS? 1) OBVIOUSLY; THE SMA DID NOT HAVE VFR SEP; BUT I MUCH PREFER NOT HAVING TO RELY ON THE OTHER FELLOW FOR SAFETY. 2) WE KNEW BEFORE PLANO FROM ATIS THAT WE WOULD BE APCHING TOWARD VFR TFC DEPARTING; YET WE PROCEEDED AS IF WE HAD GUARANTEED SEP ALL THE WAY TO THE RESTROOM. 3) APCH TURNED US LOOSE ALMOST OVER THE FAA. A LITTLE MORE TIME MIGHT HAVE HELPED. 4) TWR DIDN'T KNOW WHERE WE WERE; EXACTLY. BY THE TIME WE ALL AGREED ON OUR POS; OUR PROB HAD PASSED UNDER US. 5) CIRCLING APCHS ARE NOT EVEN FOR THE BIRDS. I DO NOT USE THEM IN RESTR VISIBILITY; OR MUCH BELOW 800' AGL. I NOW THINK THEY ARE EVEN MORE DANGERS IN BARELY VFR.