TL;DR: Rick seems to be out for about 4-5 weeks in both the TV show and the comic.
Dave Erickson, the showrunner for Fear the Walking Dead, got a word-of-god answer on this from series creator Robert Kirkman.
In his interview with Tech Insider, Erickson said:
"Robert has said for him, the coma, Rick was probably out four to five weeks," he continued. "If you count the days of season one of our show, we’re probably around week three [by the end of the season]. So ... the discovery will continue. Our characters will be up to speed, and they will know that the world has changed and the apocalypse has come, but there’s still going to be a lot of real estate to explore."
This lines up pretty well with the evidence we see in both the comics and the TV show, despite the fact that we are rarely given exact dates or timeframes in either..
First off, let's discuss the timeframe we do specifically know.
In Wildfire (S01E05), Dr. Jenner says,
It's day 194 since Wildfire was declared
Unfortunately, there is some debate regarding just how long the events of Season 1 took. But we know that it's been roughly 6 months from the time the outbreak hit until the end of the season.
Let's look further.
In the pilot, Morgan says,
Gas and light have been down for maybe a month.
This is a bit helpful, but we still don't know how long gas and light were operational before they shut down.
We do get a hint about the timeframe since the hospital was evacuated without ever really noticing it.
Notice that the lights are on.
But Morgan said that the gas and lights have been out for a while. That means that the hospital was running on a generator. That makes sense.
A quick search tells us that hospital generators can run about a day or so unattended.
This doesn't make much sense though, as it means that the hospital would have had to be refilling the generator daily for almost a month. That's a lot of fuel to stockpile, especially with the apocalypse occurring.
Ugh. OK. So, the show really doesn't give us solid info. What about the comic? Here we get a little more help.
In the comics, Morgan says that the media shut down after "a few weeks" and that they then started telling people to leave.
We're not told how long it's been since the power went out, but they seem to be eating/talking by the light of a hurricane lamp.
When Rick meets Glenn, Glenn makes a comment indicating that it's been about a month.
Where've you been for the past month?
But that's just an off the cuff remark, right?
Donna makes a similar comment when they get to the camp.
That's the best news I've heard all month!
Rick discusses what happened at the hospital with Lori.
They said people were going to stay at the hospital when they evacuated. From what you told me... they must have abandoned the hospital less than a week after we left.
So, it was "a few weeks" before the media shut down and told everyone to leave town. It was then less than a week from the time Lori, Shane, and Carl left until the hospital was abandoned.
Now, in the comics, we never see lights on at the hospital for sure, so we're back to not knowing exactly how long Rick was abandoned at the hospital, but the power is out and the facts regarding how long generators can run still applies. We've also got enough anecdotal evidence to put them at roughly a month from the outbreak until Rick wakes up.
