Growing confidence in the mechanical plug's security convinced scientists it was safe to leave it unmonitored for a few days, Retired Coast Guard Adm. Thad Allen said. He said they'll decide Thursday evening whether dozens of ships in the area will leave.
"While this is not a hurricane, it's a storm that will have probably some significant impacts, so we're taking appropriate cautions," Allen said.
The cap has been in place for a week with pressure rising, CBS News Correspondent Kelly Cobiella reports from Port Fourchon, La. Cameras on remotely operated vehicles - unmanned submarines - have spotted no major leaks or signs it's unstable.
BP executive Doug Suttles said engineers may have some data on the well but not until after the threat passes, Cobiella reports.
Forecasters at the U.S. National Hurricane Center in Miami say the storm system already has caused flooding in Puerto Rico, the Dominican Republic and Haiti. It could become Tropical Storm Bonnie later Thursday and reach the Gulf of Mexico by Saturday.
Work on plugging the well is at a standstill just days before the expected completion of a relief tunnel to permanently throttle the free-flowing crude.
If work crews are evacuated, it could be two weeks before they can resume the effort to kill the well. That would upset BP's timetable, which called for finishing the relief tunnel by the end of July and plugging the blown-out well by early August.
Even if the storm misses the area, work on the relief tunnel will be delayed by about a week, BP Vice President Kent Wells said.
Seas already were choppy in the Gulf, with waves up to five feet rocking boats as crews prepared to leave if needed. Some boats involved in the cleanup were called into port Thursday, Coast Guard Rear Adm. Paul Zukunft said.
He also directed workers to remove booms from marsh areas along the coast to prevent damage to ecologically sensitive areas.
Even if the storm does not hit the area directly, it could affect the effort to contain the oil and clean it up. Hurricane Alex stayed 500 miles away last month, yet skimming in Alabama, Mississippi and Florida was curtailed for nearly a week.
Crews had planned to spend Wednesday and Thursday reinforcing with cement the last few feet of the relief tunnel that will be used to pump mud into the gusher and kill it once and for all. But BP put the task on hold and instead placed a temporary plug called a storm packer deep inside the tunnel, in case it has to be abandoned until the storm passes.
"What we didn't want to do is be in the middle of an operation and potentially put the relief well at some risk," BP vice president Kent Wells said.
The relief tunnel extends about two miles under the seabed. It's now about four feet from the side of the well, although BP still has more than 100 feet to drill diagonally before the tunnel reaches the well. BP plans to insert a final string of casing, or drilling pipe, cement it into place, and give it up to a week to set, before attempting to punch through to the blown-out well and kill it.
The two rigs drilling relief tunnels will disconnect from the well if they have to evacuate the site. All appeared quiet on the rigs Thursday afternoon.
BP's broken well spewed somewhere between 94 million and 184 million gallons into the Gulf before the cap was attached. The crisis - the biggest offshore oil spill in U.S. history - unfolded after the BP-leased Deepwater Horizon rig exploded April 20, killing 11 workers.
The White House said Thursday President Obama and his family will vacation on the Gulf Coast next month, visiting Florida for a weekend. Both the president and first lady Michelle Obama have made a point of encouraging people to visit Gulf Coast beaches that are open and free of oil damage to help the local economy.