If the Jedi had had time, they might well have questioned it.
But remember, the battle at the end of Ep2 was a horrific disaster for the Jedi Order. That was basically a decapitation strike against Count Dooku and the Confed leadership. If they'd know they had an army, they would have brought one (as is, Yoda apparently moved incredibly fast), but without an equivalent military force (while the Senate had authorized an army, that takes time to build and train), trying to kill or capture the Confed leadership structure was their best hope for nipping the nascent rebellion in the bud. As we saw, the Jedi there were almost wiped out.
Had the Jedi been slaughtered or captured, the prestige of the Jedi Order would have plummeted, as they're obviously no longer fit to guard the Republic in these dangerous times. The only prestigious Jedi left would have been Yoda, who might well have retired in disgrace and grief (to be quietly hunted down and killed later). This would, in fact, have advanced Palpatine's agenda rather rapidly, actually. I suspect he hoped for this.
But, as happened on screen, suddenly, unlooked-for, there is a military force of stupendous proportion available for use, and already pledged to the Republic. With the knowledge that they had avoided catastrophe by the hair of Anakin's chin, the Jedi surely embraced the Clone Army as a means to keep the Republic safe and extend their fighting power. Puzzling inconsistencies (who actually started it? Why'd the prime template for the clones fight on the Confed side?) were shoved aside in gratitude that the Jedi might be able to win this one.
Brad