(CNN) -- The unique military capabilities of the United States made it the leader of initial coalition attacks on Libya aimed at establishing a no-fly zone and halting Moammar Gadhafi's forces, but the mission will soon shift to control by NATO or others with participation by Arab nations, U.S. officials insist.
From President Barack Obama on down, administration officials say U.S. forces eventually will provide a supporting role -- rather than leading the way -- in maintaining the no-fly zone over Libya and preventing Gadhafi from using his military against his people.
National Security Adviser Tom Donilon cited "a unique capability we could bring" that "enabled the other assets to be able to be brought to bear right now." After the first phase, he said, "the French and others agreed at NATO to have NATO take on the command and control of this operation at some point" within "not weeks, but days."
The overall goal is for Gadhafi to step down as Libya's leader, Donilon said in a Sunday briefing with reporters covering Obama's Latin American trip.
For now, though, the mission is based on the U.N. Security Council resolution that authorized it, as well as an Arab League endorsement for halting Gadhafi's ability to attack his people by putting in a no-fly zone and other necessary steps, according to Donilon and others.
That means the immediate goal of the mission labeled "limited" by Donilon and Joint Chiefs of Staff Chairman Adm. Mike Mullen is to halt Gadhafi's air capabilities, protect Libyan civilians and ensure that humanitarian work can proceed, they said.
Successful completion of the first phase would bring the transition in leadership, but it remains unclear whether NATO or particular nations will take control.
NATO could command the coalition's no-fly mission in Libya, but some Arab nations are hesitant to fly under a NATO banner and that has held up the move, said one official who asked not to be identified due to the sensitivity of negotiations.
"NATO has the capability to do a rapid switchover," the official said. "The problem is, they have to do everything by consensus."
Also uncertain is when that will happen. Obama and other officials have said the transfer would occur within days, but Gen. Carter Ham, the commander of U.S. Africa Command, said Monday that no timetable was possible yet.
"It's not so simple as just having a handshake someplace and saying, 'OK, you're now in charge,'" Ham said. "There are some very complex technical things that have to occur, particularly in the management, command and control of the air campaign, to make sure that, one, we have no disruption whatsoever in the ongoing operation, two, that we put none of our air crews at risk as we go through this transition to whatever that follow-on headquarters would be."
A U.S. official said Monday that the momentum of Gadhafi's forces has been stopped, with rebels now able to hold onto areas under threat of attack.
According to the U.S. official, who spoke on condition of not being identified, most people predict a "more drawn-out conflict" in Libya.
Gadhafi has some "fierce loyalists" around him, and although there have been some defections to the rebels, there haven't been any mass defections, the official said.
Some in Congress question what happens in the event of a lengthy standoff in Libya.
"I do not understand the mission because as far as I can tell in the United States there is no mission and there are no guidelines for success," Sen. Richard Lugar of Indiana, the ranking Republican on the Foreign Relations Committee, told CNN on Monday.
Sen. Mark Begich, D-Alaska, a member of the chamber's Armed Services Committee, expressed similar reservations.
"Although I do not support Gadhafi killing his own people, I have many concerns regarding U.S. involvement," Begich said in a prepared statement.
Begich questioned the risk the military action could pose for U.S. service members, how much it could cost, and, like Lugar, what the objective is.
"At this point we all hope this campaign is short-lived and that it prevents Gadhafi from slaughtering the people of Libya," Begich stated. "And I will hold President Obama to his word that no American ground troops will be sent in."
U.S. military officials including Mullen have acknowledged that the current mission could end successfully with Gadhafi still in power.
Donilon said other steps taken so far, such as stronger U.S. and U.N. sanctions and growing international opposition to Gadhafi, would ratchet up pressure on the Libyan leader to eventually step aside.
"I think he will be ... pressured, isolated, and will have to make some choices going forward," Donilon said of Gadhafi.
Another question is how much Arab support the mission has. The French Defense Ministry says Qatar has contributed four jet fighters, but another expected participant -- the United Arab Emirates -- said Monday it still was considering its role and only would provide humanitarian aid for now.
Even some NATO allies were calling for more clarity.
A spokesman for Norway's Defense Minister told CNN on Monday that "six Norwegian fighter jets sent to the international air campaign in Libya are in Crete ready to take part as soon as the formal structure of the operation and the rules of engagement have been agreed."
CNN's Pam Benson, Chris Lawrence, Tom Cohen and Laura Perez Maestro contributed to this story