Infantry is competitive. However, the Tyranny of the Thirds must be respected. That being said, it is not uncommon for the of SPCs a given training company to ensure that those, whom they prefer to enter a combat arms MOS, get those slots. Sometimes this can occur at the expense of the Almighty Thirds. There are four (4) Infantry Officer Courses (IOC) per year. Each numbers approximately 90-110 Lieutenants and usually one (1) SNCO instructor from either of the Infantry Unit Leaders Courses (IULC) (PME for Infantry Platoon Sergeants) or Advanced Infantry Training Battalions (AITB) (such as Infantry Squad Leaders Course, Machinegun Leaders Course, Infantry Mortar Leaders Course, Infantry Missilemen Leaders Course). Seven (7) Basic Office Courses feed into these 4 IOC classes. They number anywhere from 250-300 Lieutenants (consisting of Ground, Law, and Air Contracts). These numbers are likely to drop somewhat with the coming drawdown of forces. Do the math. Its definitely an achievable goal, but it requires much dedication.
N.B. If you're going to USMA, you have the other bigger hurdle to get over consisting of the cross-commission into the Marine Corps. I know of two from my contemporary class at USMA that did it. One is a Combat Engineer, the other is waiting to pick up at IOC.