FLC IN A C525 ON APCH TO TEB WERE UNABLE TO COMMUNICATE WITH THE APCH CTLR AND CONTACTED THE TWR FOR LNDG.

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CAPT AND FO WERE FLYING A CITATION JET; ACFT X; ON DEC/XA/00 ON A FLT FROM LBE TO TEB. AT ABOUT XA10; WE WERE CLRED TO 3000 FT BY NEW YORK APCH. THE ATIS GAVE THE WX BUT NOT THE TYPE OF APCH OR RWY IN USE. THE WX WAS SCATTERED; VARIABLE BROKEN AT ABOUT 4300 FT; AND APPROX 10 MI VISIBILITY. THE NEW YORK TRACON WAS EXTREMELY BUSY; AND THE CTLR WAS SO BUSY THAT IT SEEMED THAT HALF OF THE ACFT NEVER ACKNOWLEDGED HIS COMMANDS. HE WAS ISSUING COMMANDS SO FAST TO SO MANY ACFT THAT THERE WAS VIRTUALLY NOT A CHANCE TO GET A WORD IN EDGEWISE. WE WERE ASSIGNED A HDG ABOUT 12.4 MI OUT OF TEB AND ISSUED A DSCNT TO 3000 FT. WE WERE THEN ISSUED A HDG 'FOR INTERCEPT' AND A DSCNT TO 2000 FT. AT THAT TIME; WE STILL DIDN'T KNOW WHAT RWY OR APCH TO EXPECT. WE WERE THEN ISSUED A COMMAND TO 1500 FT 'NOW' AND THE CTLR HAD ANXIETY IN HIS VOICE. FO WAS FINALLY ABLE TO ASK WHAT APCH WE COULD EXPECT AND THE CTLR'S RELY WAS VOR DME ALPHA 24 APCH. THIS OCCURRED ABOUT 2 1/2 - 3 MI FROM THE ARPT. AS CAPT STARTED TO TURN FOR AN INTERCEPT TO APCH COURSE; WE BOTH LOOKED DOWN AND SAW THAT W WERE OVER THE N END OF THE ARPT; AND THE APCH END OF RWY 24 AT 1500 FT. THE CAPT THEN MADE A SLIGHT R AND TURNED L DOWNWIND. AT THAT TIME THE CAPT YELLED AT THE FO THAT WE HAVE TO TALK TO SOMEONE ASAP BECAUSE THERE WERE ACFT TO THE L AND R OF US; AS WELL AS IN FRONT XING OUR FLT PATH; AND THE 'HEAVIES' OVER THE TOP OF US GOING INTO EWR. WE WERE GIVEN NO FURTHER INSTRUCTIONS BY NEW YORK TRACON; NOR ASKED IF WE SAW THE ARPT; NOR WERE WE ADVISED TO 'TO GO TWR' FROM THE APCH CTLR. HIS LAST MESSAGE TO US WAS 'WE CAN EXPECT THE VOR DME ALPHA APCH.' UNABLE TO TALK OVER THE APCH CTLR; FO THEN WENT TO THE TWR AND WAS GIVEN THE INSTRUCTIONS TO CONTINUE DOWNWIND AND THE TWR WOULD CALL BASE AS THERE WERE 3 ACFT IN FRONT OF US. THE REST OF THE APCH AND LNDG WAS UNEVENTFUL. THIS SIT WAS EXTREMELY HAZARDOUS AND UNSAFE. WE WERE IN AMONGST OTHER ACFT AT THE SAME ALT; TRAVELING IN ALL DIRECTIONS; CLBING; DSNDING; AND NOBODY TALKING TO US OR EVEN ACKNOWLEDGING OUR POS. IN SHORT; IN ONE OF THE BUSIEST ARPTS IN THE UNITED STATES; AT A VERY BUSY TIME; WITH ARRIVING AND DEPARTING JETS ALL OVER; WE WERE EFFECTIVELY NOT UNDER POSITIVE CTL. THIS WAS TRULY A DANGEROUS SIT WHICH SHOULD NOT HAVE HAPPENED. OUR SENSE IS THAT THE CTLR; WHO SEEMED COMPETENT AND QUICK; HAD FAR TOO MANY ACFT UNDER HIS CTL; AND HE WAS UNABLE TO MANAGE ALL SIMULTANEOUSLY AND SAFELY. THE ATIS ALSO WAS MISSING INFO WHICH WOULD HAVE HELPED; SUCH AS THE APCH AND RWY IN USE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED IT WAS ONE OF THE BUSIEST PERIODS HE HAS EXPERIENCED AT TEB. HE SAID HE COULD TELL THE CTLR WAS OVERWHELMED WITH TFC AND SOUNDED AS IF HE WAS HANDLING THE TFC FREE STYLE. HE SAID THE INCIDENT WAS RPTED TO THE CHIEF PLT AND THE DIRECTOR OF OPS AND EVENTUALLY THE LCL FAA FSDO.