The apologies are out of the way and the offense forgiven. But the underlying policy argument remains, after a Congressman drew fire from both sides of the aisle for his outburst during President Obama's speech Wednesday.

Rep. Joe Wilson, R-S.C., was criticized for interrupting Obama's address to a joint session of Congress to accuse the president of lying about his health care reform plan prohibiting coverage for illegal immigrants. Wilson quickly apologized, and the White House accepted the apology.

Wilson apologized again Thursday morning, though he also says a massive loophole could wind up in the health care bill: no requirement to prove citizenship for health care coverage.

Among three House committees to pass bills for health reform, only one expressly bans federal funding for proving health coverage to illegal immigrants.

"The Congressional Research Service has indicated that indeed the bills that are before Congress would include illegal aliens," Wilson said. "And I think this is wrong."

Indeed, the nonpartisan Congressional Research Service study found that the House health care bill does not restrict illegal immigrants from receiving health care coverage.

House Republican Minority Leader John Boehner amplified the complaint that without proof of citizenship, illegal immigrants could be insured.

"There were two opportunities for House Democrats to make clear that illegal immigrants wouldn't be covered by putting in requirements to show citizenships," he said. "Both of those amendments were, in fact, rejected."

In the Senate, Democrats in the so called "Gang of Six," a group of bipartisan senators on the Senate Finance Committee which is the last panel yet to release its bill, began moving quickly to close the loophole that Wilson helped bring greater attention to.

"We absolutely assure that those who are here illegally would not get the benefit of any of these initiatives," Sen. Kent Conrad said.

House Democrats have left open the option to sanction Wilson for violating a House rule that expressly prohibits members from accusing presidents of lying. But they signaled a preference to move ahead without further distraction.

"Let's not spend time on that," House Speaker Nancy Pelosi said. "Yes, there is a procedure that could have been implemented. I think that the president did the right thing: just continued on from it and didn't give it any more attention than it deserved."

FOX News' Carl Cameron contributed to this report.