Since we know that the Pentagon has a huge propaganda apparatus to keep pleasing facts in circulation, perhaps there's not much point in fact-checking a single Dick Cheney claim to loyalists at the Manhattan Institute. But here it is --
More than 540,000 Iraqis now serve in those [armed] forces.
Here's his source; it's page 13 of a Powerpoint presentation. You get to about 540,000 if you add all "assigned personnel" and ignore the footnote --
Numbers are based upon [Government of Iraq] payroll data and do not reflect present for duty totals.
So there is not anything like 540,000 actually "serving" -- it would be news if there was. That's before one gets into the question of how many of those 540,000 are just militias working -- or collecting cheques -- out of ministries. Note the dependence of the total on numbers from the Ministry of the Interior and not the Ministry for Defence.