When Lama Su tells Obi-Wan about the clones, he explains one hundred thousand are ready, and an upcoming one million,
but you already knew that, so i'll get to the point.

In world war two, the US alone had military statistics of somewhere around seven million, 2.5 million being in the air force and navy. That's not even getting into the number in the Armed forces of larger/heavier populated countries such as the USSR and China.

Obviously, the Republic spans over hundreds of star systems, and 1million 1hundred thousand troops just doesn't seem like enough to regulate and ensure the keeping of such a large vicinity during war. Not to mention fighting the war.

The only explanation I can think of is that, the Republic has been rooted, running, and held together by Diplomacy ( with the help of the jedi )
And because of this, they were able to devote all their forces to fighting the war.
But then What would be there to stop the CIS from conquering whatever planet they please???

Basically all this in a nutshell: How was the Republic able to occupate and protect all their planets (I know the CIS did invade a lot of the planets but) AND fight a war with only 1,100,000 troops + jedi???

Thanks, and
May the Force Be With You!