June 6, 2010 -- Adm. Thad Allen says that 10,000 barrels of oil were collected Saturday using the newly installed containment cap on the gushing oil well in the Gulf and that number is expect to increase in the coming days.

The National Incident Commander told "This Week" anchor Jake Tapper that he expects the majority of the leaking oil can be contained "if the system is operating properly.

"We're not going to know how much oil is coming out until we're able to optimize the production, and that's what they're doing right now," Adm. Allen said. "They are slowly raising production. It was 6,000 a day before, and it was 10,000 yesterday."

Allen explained that despite the unprecedented clean-up efforts massive amounts of oil are still reaching the coast because "this spill is just aggregated over a 200-mile radius around the wellbore, where it's leaking right now, and it's not a monolithic spill. It is literally hundreds and thousands of smaller spills."

The size of the spills, he said, "could be anywhere from 20 to 100 yards to several miles in length."

"What we're going to have to do is not only be prepared to deal with the oil onshore, we are going to have to push it out to 50 miles offshore and basically have skimming capability that runs from southern Louisiana to Port St. Jill, Fla., and we are in the process of putting those things in place right now," Allen said. "And this is a war, it's an insidious war, because it's attacking, you know, four states one at a time, and it comes from different directions depending on the weather."

Allen said scientists are studying whether giant plumes or columns of oil are forming in the Gulf, and researchers are developing a massive model to better understand what is happening below the surface.

Sens. Cornyn and Kerry Offer Opposing Views on White House BP Response

Texas Republican Sen. John Cornyn said "BP's response has been lousy," but he was also critical of President Obama's leadership in managing the incident.

"I think, really, we need the president to step up and assert himself and to say, let's cut through the red tape, let's cut through the chain of command and let's get assets where they need to be," Cornyn said on "This Week."

Sen. John Kerry, D-Mass., also appearing on "This Week," defended the Obama administration, saying, "they are holding BP's feet to the fire."

Kerry pointed fingers at the Bush administration for lax oversight of the oil industry.

"Frankly, we had eight years, as many of us remember, of secret oil industry meetings where they wrote the oil laws, where there was an incestuous relationship with the MMS, and everybody understands this relationship has to change," Kerry said.

The oil spill has put the spotlight on a Kerry's energy and climate bill. Sen. Cornyn wouldn't back the measure, but he said he does support some aspects of the bill.

"I think rather than try to hit a grand slam home run, I'd like to work with Sen. Kerry and others to try to do, you know, hit some singles and develop nuclear power, battery technology that will help us deal with our environmental concern," Cornyn said.

Tapper also asked Adm. Allen about government workers and BP contractors working on the spill who were told not to speak to reporters. Allen said he has issued a directive that "the media will have uninhibited access anywhere we're doing operations, except for two things, if it's a security or safety problem. That is my policy. I'm the national incident commander."

The admiral pledged to get the word out to workers that they can speak publicly about their efforts.