[Did any Europeans believe that a future war wouldn't be short in 1914?] (https://www.reddit.com/r/AskHistorians/comments/3bl50d/was_there_any_way_that_europeans_in_1914_could/)
[Peace Initiatives during WWI] (https://www.reddit.com/r/AskHistorians/comments/3365de/peace_initiatives_during_wwi/)
[Diplomatically, why did WWI last so long?] (https://www.reddit.com/r/AskHistorians/comments/2yp7xj/from_a_diplomatic_standpoint_why_did_ww1_last_so/)
[When the trench stalemate set in, why did the Great Powers not make peace?] (http://www.reddit.com/r/AskHistorians/comments/36br6e/when_world_war_i_stagnated_into_trench_warfare_in/)
[An early end to WWI?] (http://www.reddit.com/r/AskHistorians/comments/39ya5k/ending_wwi_early/)
[Did German civilians believe that WWI would be 'over by Christmas'?] (http://www.reddit.com/r/AskHistorians/comments/33nejq/its_often_said_that_in_1914_the_british_public/)
These are some previous answers I've given on the subject.
In reality, there is little to no evidence that "over by Christmas" was ever a widespread saying/belief in 1914. The closest saying is Kaiser Wilhelm's informing of soldiers bound for France in August that they would "be home before the leaves fall". This, of course, refers to autumn, not late December! As far as WWI Social Historian Adrian Gregory is able to tell in his work The Last Great War, the saying only appears in Civilian writings in Britain at least later in the war, and with the typical context of mocking the overly optimistic.
No, the war would not have ended by Christmas. Even if the French had been knocked out by autumn, highly unlikely in reality, there would still have been the crumbling Austro-Hungarian Army that needed support against the Russian Army, which enjoyed stunning success outside the defeat at Tannenberg. With Britain dominating the waves, and possessing the financial resources to support the Franco-Russian Entente, the war could continue into next year and onwards. At most, the German General Staff expected an end to hostilities by 1916 perhaps; unfortunately, that proved to be the year of Verdun, the Somme, the Brusilov Offensive, and of Romania's entry into the war!
Sorry, but your submission has been removed because we don't allow hypothetical questions. If possible, please feel free to rephrase the question so that it does not call for such speculation, and resubmit Otherwise, this sort of thing is better suited for /r/HistoryWhatIf.