With the U.S. military's sizeable initial engagement in Libya to impose a no-fly zone, and with what some preceive as mixed messages from the Obama administration on an overall mission, respected moderate senators Monday began expressing concern for the road ahead in the African nation and said Congress must be more involved and the American people more informed.

"Although I do not support Qaddafi killing his own people, I have many concerns regarding U.S. involvement. As a member of the Senate Armed Services Committee, I will continue to monitor the situation and hold the Administration accountable for explaining the objective of the military campaign and other questions," declared Sen. Mark Begich, D-Alaska, a member of the Democratic leadership.

"We need to get more involved," former Vietnam combat veteran Sen. Jim Webb, D-Va., told MSNBC on Monday. "We have not had a debate...This isn't the way that our system is supposed to work."

Sen. Dick Lugar, a GOP foreign policy heavyweight, has consistently criticized the operation, calling for a vote in Congress. "My basic concern is that we do not have a plan for the United States and how its allies are going to handle the situation. We don't have objectives that, or at least some idea of how we would obtain those objectives," the Indiana senator told Fox.

"Who is in command of this operation?" Sen. Mark Kirk, R-Ill., a current U.S. Navy reservist, asked rhetorically Monday at a speech in Chicago, "I don't know. Admiral (Mike) Mullen didn't seem to give a clear answer."

Mullen, on Fox News Sunday, outlined a limited American military presence moving from a leading to a supportive role, but added, "I don't have an exact date in mind and I don't -- I haven't been given a date by the president where U.S. military participation here would end."

Sen. Kirk, who fought in NATO's military intervention in Kosovo in 1999, agreed that President Obama should seek authorization from Congress for the engagement in Libya, a vote he would support.  But Kirk told reporters that it's time for Obama to explain the situation to the American people.

"He needs to speak to the nation. A presidential address from the Oval Office is neccesary - outline the mission, who's in charge," Kirk said, adding that he thinks the mission should be to remove the mercurial Libyan leader from power, something Administration officials have said is not the current goal despite the president's recent call for Qaddafi to go.

Making clear that he intends to hold the president's feet to the fire when it comes to Obama's promise of no U.S. troops on Libyan soil, Begich added, "Congress needs to understand the risk involved to the lives of our service members, how long the Administration anticipates U.S. involvement, the impact of our involvement on our other national security priorities like Afghanistan, and what the ultimate objective is. Finally, the Administration needs to be straight with Congress and the American people about what the cost of this activity will be to American taxpayers."

Not everyone is skeptical, however, of the Administration's efforts. Sen. John McCain, top Republican on the Armed Services panel who called early on for a no-fly zone, was more concerned that the latest move could be too little, too late.

"Senator McCain is glad the administration finally took a stand against the barbaric Qadaffi regime and stood up for human rights. He believes the Administration should have acted sooner by not taking such a backseat role to our allies," the senator's spokeswoman, Brooke Buchanan, told Fox Monday.

Still, a number of members are concerned that not enough is known about the rebel force opposing Qaddafi, should the colonel step down or be removed from power, and, like Admiral Mullen, enough is not known about the end point in this conflict.

"The president and the secretary of state have a very clear obligation now to come forward to the American people and to the Congress and state clearly what they believe the end point should be. They haven't done that." Webb said.