Baloney.
Many knew exactly how bad the situation was...but Chamberlain controlled the media (sound familiar?)...so the public was kept in the dark until finally the SHTF.
The fall of France came as a surprise to most people, so it stands to reason that not everyone saw the Allies' situation as dire as it was during the "Phoney War."
Churchill changed parties several times in his career. He had been responsible for some bad policies -- the Gallipoli campaign of the First World War, the botched return to the Gold Standard in 1925. The Norwegian campaign that led to Chamberlain's dismissal was also Churchill's idea.
We know now that Churchill was a great wartime leader, but there were plenty of reasons why his contemporaries didn't entirely trust him. And if his speeches were great, we know now that people with a reputation for great oratory don't always make great leaders.