On the House floor where President Obama spoke just a half-day earlier, two words shouted by a Republican congressman reverberated louder than the finer points of the health care debate.

House Democrats seized on House rules Thursday to demand South Carolina Rep. Joe Wilson offer a high-profile apology to President Obama for shouting, "You lie," during the president's health care address.

Wilson called the White House shortly after Obama's speech to say he was out of line. The White House said early Thursday that the president accepted the apology.

But that did not put the issue to rest, and House Majority Whip Jim Clyburn, also of South Carolina, asked Wilson to apologize on the House floor in front of his colleagues. The final vote of the day was held open by Democrats to give him an opportunity to do so, but he refused. 

Democrats threatened to censure Wilson absent such an apology. So far they have not done it -- but even though House Speaker Nancy Pelosi said earlier that a censure was not being considered, her top deputies kept it in the mix. 

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House leaders debated future disciplinary steps against Wilson at a weekly closed-door strategy session in Pelosi's office Thursday.  

"I want Mr. Wilson to come to the floor of the House and apologize," said House Majority Leader Steny Hoyer. He indicated that House leaders did not reach a conclusion on sanctioning Wilson. 

"We need to figure out what to do," said one senior member of the leadership team. Another high-level House source suggested that lawmakers didn't want to let Wilson's transgression go unpunished "because of the magnitude" of the accusation directed at Obama. 

In strictly political terms, Wilson's outburst appeared to be a winner for Democrats. 

According to one Democratic source, Wilson's Democratic opponent Rob Miller had by mid-day Thursday received 5,000 new contributions worth about $200,000 in the aftermath of the outburst. The Democratic Congressional Campaign Committee was also trying to raise money off the heckling. Miller lost to Wilson in the 2008 election, 54-46 percent

Wilson's House Web site crashed after he was identified Wednesday night as the heckler and he took a beating on his Twitter page for breaching protocol. House rules expressly prohibit lawmakers from calling the president a "liar" or accusing him of "lying." 

But Wilson has tried to put the genie back in the bottle after he drew immediate, widespread and bipartisan criticism Wednesday. Shortly after the speech ended, Wilson issued a written apology and spoke with White House Chief of Staff Rahm Emanuel to say he was sorry. 

Obama on Thursday extended his forgiveness. 

"I'm a big believer that we all make mistakes. He apologized quickly and without equivocation, and I'm appreciative of that," Obama told reporters. 

In the face of persistent criticism, Republicans started to come to Wilson's defense. 

South Carolina Sen. Lindsey Graham told FOX News that Wilson should not be judged on those two words. 

"He corrected his mistake. His mouth spoke before his mind," said Rep. Kevin McCarthy, R-Calif., chief deputy whip. 

Wilson's outburst immediately followed Obama's statement: "There are also those who claim that our reform effort will insure illegal immigrants. This, too, is false. The reforms I'm proposing would not apply to those who are here illegally." 

House Minority Leader John Boehner said Thursday that, according to a Congressional Research Service report, illegal immigrants would indeed be covered, defending Wilson's assertion even though he called the manner in which he delivered it "inappropriate." 

White House Press Secretary Robert Gibbs insisted Thursday that illegal immigrants would be prohibited from buying into a health insurance exchange created by the federal government.

Wilson said Thursday he wants to have a "civil discussion" on health care, calling his comments "spontaneous." 

Democrats are walking a fine line in deciding whether to pursue a censure. While some Democrats want to punish Wilson, others are worried the action could distract from the health care reform effort. 

Obama hinted at that view when asked about Wilson Thursday. 

"I do think that, as I said last night, we have to get to the point where we can have a conversation about big, important issues that matter to the American people, without vitriol, without name-calling," he said. "The media can always be helpful by not giving all the attention to the loudest or shrillest voices and try to stay a little bit more focused on the issues at hand." 

FOX News' Chad Pergram contributed to this report.