New Orleans ? A containment cap was capturing more and more of the crude pouring from a damaged oil well in 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.

Brown Pelicans fly in front of the rising sun Sunday at Queen Bess Island, La,. Oil from the Deepwater Horizon spill continued to move inland along several Gulf states.

The spill’s harmful environmental effects also appeared to spread to Texas, with the government reporting Sunday that dead birds with oil on them were found for the first time in that state.

Allen 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 spill has also caused an environmental crisis for the region. A wildlife report issued Sunday by the government command center in Robert, La., says that two dead birds with oil on them were found in Texas, but didn’t elaborate on the circumstances. Officials at the command center could not immediately comment on the wildlife report late Sunday. Dozens of dead, oiled birds have been found in other Gulf states, the majority of them in Louisiana.

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.

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.

On Sunday, BP said it had closed one of four vents that are allowing oil to escape and preventing that water intake. The company said some of the remaining vents may remain open to keep the cap system stable.

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 existing well is plugged with cement once the relief wells have been completed.

Once the cap is fully operational, if it is ultimately successful, it could capture a maximum of 630,000 gallons of oil a day.

Besides installing the containment cap, BP officials have said they want a second option for siphoning off oil by next weekend. The plan would use lines and pipes that previously injected mud down into the well — one of several failed efforts over the past six-plus weeks to contain the leak — and instead use them to suck up oil and send it to a drilling rig on the ocean surface.

BP also wants to install by late June another system to help cope with hurricanes that could roar over the site of the damaged well. When finished, there would be a riser floating about 300 feet below the ocean’s surface — far enough below the water so it would not be disturbed by powerful hurricane winds and waves but close enough so ships forced to evacuate could easily reconnect to the pipes once the storm has passed.