OK, I watch everything again from the beginning. Here's what it looks like:

* **1x01 (Days Gone Bye):** Rick wakes up, wanders around the town and is found by Morgan. They spend the night at Morgan's house **(Day 1)**. 

  The next day he heads to Atlanta. During the car chase in the beginning, the radio dispatchers mention the car is at "Route 18, two miles west of I-85." That would place them in West Point, Georgia, which is is 1h30min away from Atlanta. Regardless, I think it's safe to assume Rick gets to Atlanta in the same day. **(Day 2)**

* **1x02 (Guts)**: Rick is found by the Survivors, and they try to escape from the building.  **(still Day 2)**

* **1x03 (Tell It to the Frogs)**: The Survivors escape from Atlanta with the Still-Alives and Rick reunites with his family. **(still Day 2)**

* **1x04 (Vatos)**: Rick et al. head back to Atlanta to save Merle and get their guns back. They return by dawn to find the camp being attacked by zombies **(Day 3)**.

* **1x05 (Wildfire)**: This happens exactly the day after the attack, according to Rick's description in the beginning of the episode. They head to the CDC and reach by nightfall. **(Day 4)**.

* **1x06 (TS-19)**: It's presumably night when the Survivors dine. **(still Day 4)** The very next morning (evidenced by the fact that some people in the group are hung over, and from what's said during breakfast), the Survivors learn how everything went down.

  They also notice the countdown. Eventually, they escape the CDC. **(Day 5)**.

So the events of the entire first season transpire in just five days according to my estimates. I will watch the second season and update this answer.