Currently, the Triumph is about 35 miles off the coast of Mobile, Alabama.
There are still several steps to go before the ship will be able to dock. It should soon meet the mouth of the channel, where another boat will meet the ship to guide it up the channel to the cruise terminal. Then they'll have to go through the slow process of getting all the passengers off.
As the crippled Carnival cruise ship limps closer to the shore, relatives of some of the three thousand passengers are eagerly awaiting its arrival.
Mary Poret and Kim McKerreghan's young daughters are both on the ship. The two women drove nearly eight hours from Lufkin, Texas to Mobil to pick up their girls after hearing from them this week.
"She was scared. Her biggest fear was she didn't know if she would see me again," said Poret. "As a parent that's hard because you don't know. I mean you have to reassure a child and don't know the answer."
At least three other Carnival ships have dropped off supplies and some food to the Triumph. But passengers who've been able to text or email describe using plastic toilets and a stench so bad it's made some sick.
Jamey Kenny, is the wife of a passenger stuck on the ship and is scared about the conditions her husband has been living in. She says she's livid over Carnival's response.
"I don't think I've ever been this passionately disgusted in anything in my life," she said. "If ships were delivering cargo and food and supplies to them, why couldn't they go and drop their passengers off in Cozumel? There's got to be a way to get them off than five days, five days of conditions of no AC, no running water, no toilets."
Carnival's CEO, Micky Arison also ignited controversy after a picture surfaced of him sitting courtside at a Miami Heat basketball game Tuesday night. Arison is also the team's owner.
Relatives did say the company has been more responsive in the past couple of days, but they're tired of waiting on tugboats to slowly drag the ship back to safe harbor.
"I just think, we have more resources and people are smarter than that. And I think Carnival just missed the boat on that one. Hmm, no pun intended," said Kenny.