As someone who knows just a bit about British politics and politicians in the era before World War II, I would like to offer a different comparison. I think that, rather than Churchill (who served in the cavalry, in three different conflicts, two imperial wars, the third the Boer War; Churchill also wrote numerous books and quite literally thousands of magazine articles, and won the Noble Prize for literature), Bush shares certain qualities with two other British Prime Ministers, the egregious Stanley Baldwin, and that personification of the Peter Principle, Neville Chamberlain.
By 1936, Churchill was at the end of his tether with Baldwin government. He had created a network of career bureaucrats who gave him information, quite a bit of it secret, on the British government's refusal to deal adequately with the growing German threat. Emerging slowly from the shadow of his resistance to Indian Commonwealth status (the issue which drove him into the political wilderness, leaving office because of his resistance to independence for India), his continual badgering on the issue was starting to take hold, and he forced an open debate on British defenses. The debate is what Churchill biographer Roy Jeynkins called a "set-piece" - one of those events that become memorable precisely because it seems innocuous, but gains a momentum and provides political theater and has serious implications for national governance.
After dealing a blow to the prevarications of the First Lord of the Admiralty, Churchill turned his substantial gifts upon the Prime Minister himself. Eighteen months before, Baldwin had pledged not to allow British rearmament to fall behind the pace of German rearmament; in Britain at the time, such a public pledge was a sacred vow. Now, Churchill was showing that, in fact, British rearmament was not only behind Germany, but lagging further and further behind. His charge was a serious one - he was accusing the PM not only of lying, but of deceiving the public over the entire issue for the whole course of the eighteen months since his initial pledge.
Baldwin's response to Churchill was the wrap-up to the debate, and, combined with the pressure he was getting from King Edward VIII to marry Wallis Warfield Simpson (Baldwin's health was broken by his struggle with the king, which led to the abdication crisis and the rise of George VI), was one of the great career- and legacy-destroying moments of any politician's career. He admitted, in essence, that he had not pursued a policy of rearmament in the face of continued Nazi war preparation not out of any ideological avoidance of war, but rather to hold onto office.
Supposing I had gone to the country and said that Germany was rearming and that we must rearm, does anybody think that this pacific democracy would have rallied to that cry at that moment? I cannot think of anything that would have made the loss of the election from my point of view more certain.(Stanley Baldwin, quoted on pp. 217-218 of Alone: Winston Spencer Churchill, 1932-1940 by William Manchester
Even more than Chamberlain's school-boy approach to the brutality of Mussolini and Hitler, Baldwin's crass cowardice for party political profit did more to destroy British defenses in the face of the oncoming threat of fascism than any single factor. More important, he did so not out of any serious attachment to pacifism (admittedly, a popular position in the period between the two World Wars), but out of fear of the British public reaction to a serious consideration of the realities they faced, and how that reaction would create electoral results that were antithetical to the continuation of his National Government. Baldwin's admission was shocking to the entire country (Britain at the time had an engaged public, and the press, while subservient to power, still quoted whole speeches on its interior pages) and, combined with the deterioration of his health from the coming abdication crisis, led to his leaving office and the retirement hom of the House of Lords as Earl Baldwin of Bewsley.
Chamberlain, of course, was not so much a coward, as simply one unfit by temperament, intellect, and personality to face the challenges of the horrors coming. A man too small for the office he occupied, and comforted in power by sycophants who played upon his insecurities to ingratiate themselves as "yes-men", he was undone by events, even as he continued to believe events would vindicate him. Indeed, he left office in 1940 still convinced that a deal could be struck with Hitler, wondering why Churchill wanted to fight a war he, Chamberlain, was convinced Britain would lose (that he played no small part in creating the situation where Britain could lose was simply not a part of his thinking).
Lying, cowardly, almost amorally concerned with clinging to office and power at the expense even of national survival, convinced by turns of their own cleverness and intelligence and the soundness of their judgment, even in the face of overwhelming evidence to the contrary, neglecting the military even as they pledged to support it - these are all familiar qualities and issues for contemporary Americans, and they resonate not with Churchill, but with Baldwin and Chamberlain. History can be a good guide for understanding the present, but only when it is considered properly.