Originally posted by joespaniel
Everything I've read says the opposite. It took over a month to regain the ground lost and another six weeks to reconstitute the front line units, most of which suffered huge casualties.
In the words of the offical US Army history of the battle
The Ardennes: Battle of the Bulge "The material losses inflicted by German action [during the Battle of the Bulge] represented only a temporary dimuation of the fighting strength of a few of the American divisions and were normally replaced within a fortnight".
At the conclusion of the battle the casualties were 81,000 U.S. with 19,000 killed, 1400 British with 200 killed, and 100,000 Germans killed, wounded or captured.
The offical history gives American battle casualties as:
total: 41,3155
killed in action: 4,138
wounded in action: 20,231
missing in action: 16,946 (most of whom would have been captured)
During the period of the battle, the US Army formations in the Ardennes recieved 31,505 individual replacements to make up these losses.
(all figures are from page 674)
While there were doubtless thousands more casulties from the cold, accidents and the like, it's hard to say what proportion of these can be attributed to the German's decision to go on the offencive.
Unfortunetly, the book doesn't offer a definitive figure for the German losses, observing that, on average, each German division involved in the battle took about 2,500 casualties (these would have been much higher in some formations then others). Your figure for total casualties is undoubtably more accurate then mine though - the Offical History says that the total German strength at the start of the offencive was about 200,000 men

(as compared to about 83,000 Americans).
I can't find figures for German equipment losses, but they must have been considerable - for example, the US 2nd Armoured Division claimed the destructionof 82 German tanks, 83 artillery guns and over 400 trucks in a matter of days (see page 574). Given that the Germans had almost no ability to make good these losses and issue them to units at the front, such losses would have been crippling - 82 tanks would have been the best part of a Panzer division for example.*
In terms of damage to a formations, the history states that a single US infantry division was destroyed, and two divisions, along with an Armoured Combat Comand were temporarily crippled.
Considering that during the fighting on the West Wall the casualty ratio was undoubtably going against the Allies, and they
still hadn't satisfactorally breached the wall by the time of the German attack, I can't see how there could be any argument that the Allied victory during the Battle of the Bulge shortened the war. Aside from the mathematics, the fact that the Germans utterly wasted their last throw of the dice (which would have fallen somewhere) can only have shortened the war. If those units had been, say, lurking behind the Rhine when the Western Allies staged their crossing, or been positioned to oppose the Soviet Vistula-Oder operation then the war could easily have been extended for a few more horrible months while the Allies licked their wounds.
Indeed, some people even believe in a conspiracy theory where Eiesnhower ordered a blind eye to be turned to the German preperations in order to ensure that they launched an attack, so that their formations could be destroyed in the open! (I don't believe this myself - the Allied reserves were out of place, and any relevant files would have been declasified by now).
*Incidently, the 2nd Armoured Division's losses during the same period were 5 light tanks and 22 medium tanks, which should provide some food for thought for those folks who seem to think that American armour always took heavy losses when fighting German armour. (personel casualties were even lower: 17 KIA, 26 missing and 201 wounded). It should be noted though that the 2nd Armoured was a
very good division.