But under federal law -- the War Powers Resolution of 1973 -- Obama is only allowed to keep U.S. forces engaged in hostilities for 60 days, unless Congress declares war, authorizes funding for the effort or extends the deadline.
Congress has not enacted legislation authorizing military involvement in Libya, and the White House has not made a public effort to comply with the rule.
Experts say this is the first time an American president has defied the War Powers Resolution's deadline for participation in combat operations without any concurrent steps by Congress to fund or otherwise authorize the role.
While every administration since 1973 and some lawmakers have questioned the constitutionality of the resolution's infringement on executive power, it has not been successfully challenged in court and remains the law of the land.
Now some members of Congress from both parties want answers.
"As recently as last week your administration indicated use of the U.S. armed forces will continue indefinitely. Therefore, we are writing to ask whether you intend to comply with the requirements of the War Powers Resolution," six Republican senators wrote Wednesday in a letter to Obama. "We await your response."
Sen. Richard Lugar of Indiana, the ranking member of the Senate Foreign Relations Committee, did not co-sign the letter but has been pressing the administration to seek Congressional authorization on Libya for weeks.
"Extended engagements in military action abroad, and the costs and risks they entail, must be undertaken only with the full support of the American people," Lugar said last week.
U.S. involvement in the Libya operation is estimated to have cost taxpayers at least $750 million so far, according to the Pentagon. U.S. drones and military aircraft, including refueling tankers and surveillance planes, remain actively involved in enforcing a no-fly zone above Libya.
White House press secretary Jay Carney has said that the administration plans to continue "consultations" with Congress on Libya but would not comment when asked recently about the passing of the 60-day deadline.
But Deputy Secretary of State James Steinberg told a Senate panel last week that Obama remains "mindful" of the War Powers Resolution and seeks to abide by it.
"He will continue to do so, and we look forward to continuing to consult with Congress on our role in the coming days," he said.
With the House of Representatives on recess and Obama headed to Europe next week, many observers don't see a speedy resolution to the issue and expressed disappointment at the impasse.
"They're making a mistake on the War Powers Act," said Brookings Institution foreign policy fellow Michael O'Hanlon. "Congress does deserve a role in this and making the case to Congress for continued military action in Libya shouldn't be hard."
Tom Donnelly, director of Center for Defense Studies at the right-leaning American Enterprise Institute, speculated that Obama has tried to avoid the issue of extending operations in Libya given public sentiment on the conflict.
"There's been rising domestic and political discontent about it," he said. "Maybe he [Obama] can get away with it because of the Osama bin Laden killing. But it's difficult to say in the games of chicken between the White House, Capitol Hill and all over town."