The storm's center was located off of Florida, about 165 miles east-southeast of the mouth of the Mississippi River on Wednesday.
The depression weakened slightly on Wednesday morning, but the National Hurricane Center in Miami said it could still become Tropical Storm Danielle before reaching the coast.
Retired Coast Guard Adm. Thad Allen, the government's point man on the spill, said the last steps will have to wait for ending any threat from the well that spewed more than 200 million gallons of oil over three months before a temporary cap sealed it in mid-July.
Crews will place a temporary plug atop what they're already drilled to keep their work safe, but they won't have to remove the drill or send workers back to land. They have about 30 to 50 feet left to drill.
Once the relief well is finished, BP plans to pump mud and cement into the broken one from deep underground for a so-called "bottom kill," which will be a permanent seal.
Allen has insisted for days that BP go ahead with the bottom kill, even though the top plug appeared to be holding.
- The delay from the storm came on the same day that anglers and tourism operators got some good news: Federal authorities announced that about 5,000 square miles of Gulf along Florida's Panhandle was reopened for commercial and recreational fishing.
- The spill started with an April 20 explosion that sank the BP-leased drilling rig Deepwater Horizon and killed 11 workers. More than 300 lawsuits filed in the aftermath against BP and other companies will be handled by a federal judge in New Orleans, a judicial panel said Tuesday.
The Associated Press contributed to this report.