Regardless of their propaganda, did any of the warring nations' governments believe that WWI would be over within a few months?

The only reason for going to war was a western defence pact. To this day no one really knows why the conflict escalates ted out of control and why it wasn't settled by diplomacy. No one expected it to let years. A bit like the American Civil War of 1861-1805.

Yes. Both sides thought the war would be over quickly and that they would prevail. They thought they would just go on the offensive, capture the enemies cities and that the war would be concluded. Neither side envisioned trench warfare which was caused by the use of machine guns and there was no practical way at the time of breaking the stalemate that this technology caused. The last major European war before WW1 was the Franco-Prussian war in 1870 and the war only lasted 6 months. This was the warfare that both sides were expecting but this occurred before the Maxim Machine gun was invented in 1884, and this type of design and the wide scale deployment of similar weapons completely changed warfare.