The Omaha project is a top-secret military operation that may or may not have future relevance in the Chuck plotline. Omaha was first mentioned in "Chuck Versus the Alma Mater" where Professor Flemming explains to Bryce that the CIA needs Chuck for the Omaha project:
Bryce: Chuck Bartowski? He never got your message.
Flemming: What are you talking about?
Bryce: You put Chuck on the CIA recruitment track.
Flemming: It's not up to me, Bryce. They want him for the Omaha project.
Bryce: That's a military operation. They'll turn Chuck...
Flemming: I'm required to send all the top test results to the agency.
Bryce: I want my friend out of this.
Another possible reference is made in "Chuck Versus the Nemesis" where Bryce tells Sarah "We will always have Omaha" (a Casablanca reference, originally "We will always have Paris"). Whether Omaha was intended to have any relevance in season 2 or whether the possible plot-line was killed off due to the writers' strike is unknown.
One interesting point that could be made is that if Sarah and Bryce met on the Omaha project that Chuck was supposed to be sent to then Bryce took more than a career path from him, he took his future love life as well. Especially if there were a limited number of available spots and Bryce was only sent there once Chuck was out of the running.
There is a possibily that the Omaha Project was somehow connected with the Intersect since Professor Flemming says that Chuck is a perfect candidate because the "Keywords in his essay responses correlated with 98% of the subliminal images in the exam" and he emphasised that "the agency is not gonna let go of a recruit this promising" because of the amount of information Chuck can retain. This would also explain further why Bryce chose Chuck as the recipient of the Intersect.