Washington (CNN) -- The exact timing of a Senate vote on a resolution to back U.S. military action in Libya is not decided, Senate Majority Leader Harry Reid said Tuesday, adding the vote would not come this month.
Specifically, he said the vote would not happen before the Memorial Day recess, which begins when senators leave this week and is scheduled to run through June 5.
Veteran U.S. Sens. John Kerry, D-Massachusetts, and John McCain, R-Arizona, formally introduced a bipartisan resolution Monday expressing Congress' support for U.S. military action in Libya, laying the groundwork for what could be the first congressional action on the mission since it began more than two months ago.
The resolution falls short of explicitly giving the president congressional authorization for U.S. military involvement in Libya.
Friday marked a 60-day deadline that, under the War Powers Act, required President Barack Obama to get congressional authorization for the war in Libya or begin to withdraw troops.
The president never met that deadline, but late Friday, he sent a letter to congressional leaders endorsing the Libya resolution Kerry and McCain had been working on as something he would welcome.
"It has always been my view that it is better to take military action, even in limited actions such as this, with congressional engagement, consultation, and support," Obama wrote in the letter.
The resolution by Kerry and McCain, which they had been working on for some time but until Monday had not made public, is not a formal authorization of military action in Libya. The resolution makes no mention of the War Powers Act.
It "supports the limited use of military force by the United States in Libya as part of the NATO mission to enforce United Nations Security Council Resolution 1973 (2011), as requested by the Transitional National Council, the Arab League, and the Gulf Cooperation Council."
It also calls on the president to:
-- Submit to Congress a description of U.S. policy objectives in Libya, both during and after the rule of Libyan leader Moammar Gadhafi, and a detailed plan to achieve those objectives
-- Consult regularly with Congress regarding U.S. efforts in Libya.
As for House action, Kevin Smith, spokesman for House Speaker John Boehner, told CNN Monday, "No decisions have been made about how to proceed and we'll discuss it with our members."
Earlier, House Majority Whip Eric Cantor suggested Libya may be addressed in an amendment as part of a broader House debate this week on a defense bill, but it's unclear what the language would be, if included.
In a statement announcing the resolution, senators said they sought strong bipartisan backing for the Libya mission.
"The country is on the strongest footing when the president and Congress speak with one voice on foreign policy matters," Kerry said in the statement. "I'm pleased to have worked on this resolution with a strong bipartisan coalition and I welcome debate and congressional action on this important issue."
CNN Congressional Producer Ted Barrett contributed to this report.