The cap over a blown-out oil well is capturing more and more of the crude pouring into the Gulf of Mexico, but that bit of hope was tempered Sunday by a sharp dose of pragmatism as the federal government's point man warned the crisis could stretch into the fall.

The inverted funnel-like cap is being closely watched for whether it can make a serious dent in the flow of new oil. Coast Guard Adm. Thad Allen, overseeing the government's response to the spill, reserved judgment, saying he didn't want to risk offering false encouragement.

Instead, he warned on CBS' "Face the Nation" that the battle to contain the oil is likely to stretch into the fall. The cap will trap only so much of the oil, and relief wells being drilled won't be completed until August. In the meantime, oil will continue to spew out.

"But even after that, there will be oil out there for months to come," Allen said.

"This will be well into the fall. This is a siege across the entire Gulf. This spill is holding everybody hostage, not only economically but physically. And it has to be attacked on all fronts," he said.

Since it was placed over the busted well on Thursday, the cap has been siphoning an increasing amount of oil. On Saturday, it funneled about 441,000 gallons to a tanker on the surface, up from about 250,000 gallons it captured Friday.

But it's not clear how much is still escaping from the well that federal authorities at one point estimated was leaking between 500,000 gallons and 1 million gallons a day. Since the spill began nearly seven weeks ago, roughly 23 million to 49 million gallons of oil have leaked into the Gulf.

The prospect that the crisis could stretch beyond summer was devastating to residents along the Gulf, who are seeing thicker globs of oil show up in increasing volume all along the coastline.

In Ruth Dailey's condominium in Gulf Shores, Ala., floors already are smeared with dark blotches of oil, she said, and things are only going to get worse.

"This is just the beginning," she said. "I have a beachfront condo for a reason. With this, no one will want to come."

Kelcey Forrestier, 23, of New Orleans, said she no longer trusts the word of either BP or the U.S. government in laying out the extent of the spill. But it is clear to Forrestier, just coming in off the water at Okaloosa Island, Fla., that the spill and its damage will last long into the future.

"Oil just doesn't go away. Oil doesn't disappear," said Forrestier, who just earned a biology degree. "It has to go somewhere and it's going to come to the Gulf beaches."

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.

Allen was reluctant to characterize the degree of progress, saying much more had to be done.

"We need to underpromise and overdeliver," he said.

BP engineers must next try to close vents on the containment cap that are allowing oil to escape and preventing that water intake. 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.

The cap was only the latest effort by BP PLC to attempt to contain the leak since the Deepwater Horizon rig exploded 50 miles off the coast of Louisiana on April 20, killing 11 workers. In the past week, greater and greater quantities of thick oily sludge began making its way farther east, washing up on some of the region's hallmark white-sand beaches and coating marshes in black ooze.

Already, cleanup crews along the coast were struggling to keep pace with oil washing up thicker and faster by the hour. The sight and smell of oil undermined any consolation offered by reports of progress at the wellhead. Instead, Gulf residents voiced frustration with the apparent holes in cleanup efforts.

At Gulf Shores, Dailey walked along a line of oil mixed with seaweed that stretched as far as the eye could see. Collecting bits of the rust-colored oil did nothing to ease her anger. Clumps of seaweed hiding tar balls make the scene appear better than it really is, she said. Pick up a piece of weed and often there's oil underneath.

"They're lying when they say they're cleaning these beaches," said Dailey, of Huntsville. "They're saying that because they still want people to come."

Eventually, workers used a big sand-sifting machine to clean the public beach, leaving it spotless, at least for a while.

But a couple miles away, workers cleaning a section of sand at a state park finished their work and left their refuse on the beach in the way of the incoming tide.

"Waves are washing over plastic bags filled with tar and oil. It's crazy," said Mike Reynolds, a real estate agent and director of Share The Beach, a turtle conservation group.

At Pensacola Beach, Fla., the turquoise waves also were flecked with floating balls of tar. Buck Langston, who has been coming to the beach to collect shells for 38 years, watched as his family used improvised chopsticks to collect the tar in plastic containers.

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

As hundreds of cars streamed through the toll booths at the entrance to the beach, a protester stood at the side of the road wearing a gas mask, lab coat, latex gloves and holding a "Drill Baby Drill" sign with tea bags hanging from the edges.