NEW ORLEANS -- A device that's now sucking up significant amounts of the oil spewing from the bottom of the Gulf of Mexico offered a measure of optimism Sunday even as the government's point man on the spill warned problems would persist for months.

Coast Guard Adm. Thad Allen said on CBS' "Face the Nation" that the spill, which is ravaging beaches and wildlife, will not be contained until the leak is fully plugged and that even afterward "there will be oil out there for months to come."

The disaster, which began with an oil rig explosion in mid-April, will persist "well into the fall," Allen said.

A containment cap placed on the gusher near the sea floor trapped about 441,000 gallons of oil Saturday, BP spokesman Mark Proegler said, up from around 250,000 gallons of oil Friday. It's not clear how much is still escaping; an estimated 500,000 to 1 million gallons of crude is believed to be leaking daily.

BP chief executive Tony Hayward told the BBC on Sunday that he believed the cap was likely to capture "the majority, probably the vast majority" of the oil gushing from the well. The gradual increase in the amount being captured is deliberate, in an effort to prevent water from getting inside and forming a frozen slush that foiled a previous containment attempt.

The next step is for BP engineers to attempt to close vents on the cap that allow streams of oil to escape and prevent that water intake, and Hayward told the BBC that the company hopes a second containment system will be in place by next weekend. Allen told CBS that the oil would stop flowing only when the leak was plugged with cement.

Hawyard, who has faced criticism over his company's response to the spill, told the BBC that he wouldn't step down and that he had the "absolute intention of seeing this through to the end."

"We're going to clean up the oil, we're going to remediate any environmental damage and we are going to return the Gulf coast to the position it was in prior to this event," he told the BBC.

Allen took issue on CNN's "State of the Union" on Sunday with BP officials who said they were pleased with results of the latest effort. He said progress was being made, "but I don't think anybody should be pleased as long as there is oil in the water."

He said on "Fox News Sunday" that he doesn't "want to create any undue encouragement" and that "we need to underpromise and overdeliver."

While BP plans to eventually use an additional set of hoses and pipes to increase the amount of oil being trapped, the ultimate solution remains a relief well that should be finished by August.

The urgency of that task was apparent along the Gulf Coast nearly seven weeks after the BP rig exploded April 20, killing 11 workers and rupturing the wellhead a mile below the surface. Since then, millions of gallons of oil have been rising to the surface and spreading out across the sea.

The oil is coating and miring waterfowl in the sticky mess, and dead birds and dolphins are washing ashore. Scientists say the wildlife death toll remains relatively modest, though, because the Deepwater Horizon rig was 50 miles off the coast and most of the oil has stayed in the open sea.

The oil has steadily spread east, washing up in greater quantities in recent days. Small tar balls have washed up as far east as Fort Walton Beach, about a third of the way across the Florida Panhandle. Government officials estimate that roughly 23 million to 49 million gallons have leaked into the Gulf.

A line of oil mixed with seaweed stretched all across the beach Sunday morning in Gulf Shores, Ala. The oil was often hidden beneath the washed-up plants. At a cleaning station outside a huge condominium tower, Leon Baum scrubbed oil off his feet with Dawn dishwashing detergent.

Baum had driven with his children and grandchildren from Bebee, Ark., for their annual vacation on Alabama's coast. They had contemplated leaving because of the oil, but they've already spent hundreds of dollars on their getaway.

"After you drive all this way, you stay," Baum said.

At Pensacola Beach, Buck Langston and his family took to collecting globs of tar instead of sea shells on Sunday morning. They used improvised chopsticks to pick up the balls and drop them into plastic containers. Ultimately, the hoped to help clean it all up, Langston said.

"Yesterday it wasn't like this, this heavy," Langston said. "I don't know why cleanup crews aren't out here."

With no oil response workers on Louisiana's Queen Bess Island, Plaquemines Parish coastal zone management director P.J. Hahn decided he could wait no longer, pulling an exhausted brown pelican from the oil, slime dripping from its wings.

"We're in the sixth week, you'd think there would be a flotilla of people out here," Hahn said. "As you can see, we're so far behind the curve in this thing."

At the mouth of Alabama's Mobile Bay, hundreds of seagulls squawked on a beach dotted with countless small tar balls but not a cleanup crew in sight.