There are several issues with this question. First and foremost, historians are neither mind-readers nor time travelers, so they are unable to address such posed question directly as they are unable to actually know what people i the past were thinking (interview with people who still live may provide some insight into given topic, but they are not as good as verifiable facts, as memory problems, self-deception and common lies are always a factor). This said, I find the number quite curious, as Hitler was fond of the term 'Tausendjähriges Reich' or 'Thousand years-old state' he used in the official speeches. For example, during the annual NSDAP rally in 1934, after securing the position of a Chancellor and Reichsführer, Hitler said that 'for the next thousand years, there won't be another revolution in Germany'. This was, as far as we know it, a rhetorical figure rather than any literal belief, especially given that according to Speer, Hitler had realistic views of political stability and said that "[...]the purpose of Third Reich building projects was to transmit his time and its spirit to posterity. Ultimately, all that remained to remind men of the great epochs of history was their monumental architecture[...]” and that the inevitable ruins of the Third Reich shall "speak to the conscience of future generations of Germans”. [1]

Besides being a well-sounding expression evoking belief in long, stable existence of the country, one thousand years was referring to historical events, usually well-known by general population. Hitler and his party often used rhetorics and symbols heavily inspired by the Rome that in common opinion also existed for roughly 1000 years ('Ancient Rome' is generally associated with the period between foundation of the city allegedly 753 BC until deposition of Romulus Augustulus in 476 AD). The Holy Roman Empire also existed for similar amount of time (especially when counted from coronation of Charlemagne in 800 or Treaty of Verdun in 843. This way, Hitler was presenting future of his country by comparing it with legendary glory of Roman Empire and also as a continuation of the Holy Roman Empire that was to exist for 'another thousand years'.

Sometime you may also find the theory that the number was inspired by the medieval chiliastic movements considering 'a millennium' to be a mythical period of the ultimate development of the society followed by the Final Judgement or the period between the Second Coming of Christ and the Judgement Day, but there is little proof that Hitler or other NSDAP members were actually referring the millennarist sentiments or that knowledge of such movements was widespread enough to be of any use in propaganda.

[1] Scobie, A. 'Hitler's State Architecture - The Impact of Classical Antiquity', Pennsylvania State University Press, 1990.