Alan You hit on a few points that are interesting. Bruce has the on point response as to the success of the Price Raid: That Price simply did not have the manpower or the resources to stay in Missouri. However, there were other factors at play at that time in the war. Prior to the Price raid there had been three otheres, Marmadukes 1st Raid in January '63' involving a heavy loss of manpower during that raid, The April '63' raid into the boot heel region, and then Shelby's so called great raid. In each case these raids achieved very little in the way of strategic gains.
In the case of Price's Raid - and that is what it was - Price gained recruits mostly by drafting them as they went through every town in their path. The records are very clear on this. What was Price going to do with them once he got them back into Arkansas? There simply was no resources. The political effects was the real intention, but by the time of the Price Raid, the union high command knew how to deal with these excursions and did so quite well. Despite the claims of the post war writers most of these raids achieved very little but did keep the war alive. In many cases the raids provided a means for Missourians to simply desert. The Mine Creek Book will provide an overview and a decent one, but there has been much more in the way of work done on the subject.

One last point, at that stage of the war, why not invade Missouri. The union troops in Arkansas was incapable of stopping it and the dieing confederacy had to do something.