^ these answers I've given should be pertinent
Ronald Andidora's [Autumn 1944: Boldness is Not Enough] (http://strategicstudiesinstitute.army.mil/pubs/parameters/Articles/1987/1987%20andidora.pdf) and Roland Ruppenthal's [Logistics and the Broad Front Strategy] (http://www.history.army.mil/books/70-7_18.htm) underline the logistical difficulties that militated against Market Garden. Allied supply lines still stretched all the way back to Nomandy, and the Canadian 1st Army was occupied with German resistance in the Channel Ports and the Breskens Pocket, so it was doubtful that Antwerp would be opened any time soon to help relieve the supply crisis. Simply to provide British Second Army with the logistical support necessary to execute the operation required the suspension of other efforts on the part of the 12th and 6th Army Groups.
On top of this, the Germans had already begun to bounce back, with the influx of reserve units and newly raised forces such as Kurt Student's 1st "Parachute Army", and combined with the successful withdrawal of 80 000 troops of the German 15th Army from the Breskens Pocket, meant that the density of German forces facing 21st Army Group (1st Canadian and 2nd British Armies) and their quality was increasing. Monty's plan involved advancing on an extremely narrow front, on a highway that was to become crowded with supply columns and reinforcement/follow up units, and then somehow these forces were to sweep into the Ruhr and end the war before Christmas 1944?
Given the state of Allied logistics, the strengthening of German resistance, and the immense risk and effort that would have been and was involved in trying to prosecute the operation successfully, Market Garden really was "A Bridge Too Far."
TL;DR: No, the war could not have ended by Christmas
Without detracting from Dux's quite correct answer to the question of ending the war, it is worth pointing out that the primary goal of MG was not to end the war faster, but instead to set the conditions for clearing out the German forces which were blocking access to shipping to Antwerp. Capturing Arnhem bridge would certainly have been a boon, but the much derided claim about MG being 80% successful did have merit. The push by XXX Corps over the airborne carpet got far enough that it placed allied forces in a position to turn West into Beveland. In this, it achieved Eisenhower's primary objective.
Source: Crusade in Europe, Eisenhower.