ARTCC CTLR ISSUED IMPOSSIBLE CROSSING RESTRICTION.

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WE WERE AT FL230 NAVIGATING OUTBND ON THE HGR 113 DEG R AND TALKING TO WASH CENTER ON FREQ 133.0 ENRTE TO BWI. THE CAPT WAS FLYING WHILE I WAS HANDLING RADIO COMS. THE CAPT'S #1 NAV WAS TUNED TO HGR VOR 113 DEG R WHILE MY #2 NAV WAS TUNED TO EMI VORTAC. WASH CENTER CALLED AND TOLD US TO CROSS 45 DME W OF BALTIMORE AT 14000' AND 250 KTS. AT THAT TIME I READ BACK THE CLRNC WHILE TUNING MY #2 NAV TO BAL VORTAC AND SIMULTANEOUSLY THE CAPT STARTED A DES. MY #2 NAV LOCKED ON BAL IMMEDIATELY AND THE DME LOCKED ON JUST A FEW SECS AFTERWARDS SHOWING 56 DME FROM BALTIMORE. IMMEDIATELY I HAD THOUGHT WE WERE PICKING UP A BAD DME SIGNAL. I TUNED TO MONITOR AND CALLED WASH CENTER BACK TO VERIFY THE DISTANCE FROM BALTIMORE. HE DID NOT ANSWER. I CALLED WASH CENTER AGAIN AND ASKED HIM AGAIN TO VERIFY THE DME FROM BALTIMORE AND THAT WE WERE NOW SHOWING 54 DME AND THAT IF IT WERE CORRECT WE WERE NOT GOING TO BE ABLE TO COMPLY WITH THE PREVIOUS CLRNC AND THAT WE WILL NEED A NEW ONE. WASH CENTER THEN CALLED BACK AND SAID HE SHOWED US AT 53 DME AND FOR US TO TURN LEFT TO A HDG OF ABOUT 100 DEGS AND TO INTERCEPT THE HGR 113 DEG R TO THE BAL 331 DEG R AND FLY THAT INBND. I READ BACK THE CLRNC AND I DO BELIEVE I TOLD CENTER AGAIN THAT WE WERE NOT GOING TO MAKE IT 45 DME OUT OF BALTIMORE AT 14000' AND 250 KTS. WE WERE AT CRS SPD 320 KTS WHEN CLRNC WAS RECEIVED. A VERY SHORT DISCUSSION WITH THE CAPT WHILE HE TURNED TO A 100 DEG HDG VERIFYING WE WERE NAVIGATING ON THE HGR 113 DEG R JUST SLIGHTLY RIGHT OF COURSE. I CALLED WASH CENTER BACK AND TOLD THEM AGAIN THAT WE WERE UNABLE TO COMPLY WITH XING RESTRICTION AND THAT OUR DME SHOWED US AT THE BAL 45 DME AND DSNDING THROUGH 19000'. WASH CALLED BACK AND GAVE US A DES TO 11000'. I THEN CALLED WASH CENTER BACK AND READ BACK THE CLRNC AND ASKED HIM ABOUT THE ALT AND SPD AND HE TOLD US TO DO THE BEST WE COULD. SINCE WE HAD ALREADY BEEN DOING THE BEST WE COULD (PWR AT IDLE DES AND AROUND 4000 FPM OR BETTER DES); THE CAPT AND I DISCUSSED IT AND KNEW THAT THE XING AND SPD RESTRICTIONS WERE UNOBTAINABLE. UPON RECEIVING THE INITIAL CLRNC WE THOUGHT MAYBE THE CTLR JUST FORGOT TO GIVE IT TO USE EARLIER. THE REASON HE DIDN'T RESPOND TO OUR INITIAL CALL ASKING HIM TO VERIFY THE DME FROM BAL IS THAT IT WAS POSSIBLE HE WAS ON THE LANDLINE WITH BAL APCH LETTING THEM KNOW WE PROBABLY WOULDN'T MAKE THE RESTRICTION. LIKE I SAID; THIS IS A POSSIBILITY. IT ALL HAPPENED IN A SHORT AMOUNT OF TIME. AGAIN: THE SITUATION WAS THAT WE RECEIVED A XING AND SPD RESTRICTION TOO LATE TO COMPLY WITH.