President Obama can't hold off Congress much longer.

In the form of hearings, media appearances and possibly a vote, Congress is determined to have its say on the Libyan conflict when lawmakers return to Washington next week.

Lawmakers on both sides of the aisle have been grumbling ever since the president ordered U.S. missile strikes on Muammar al-Qaddafi's regime in support of a U.N.-authorized no-fly zone Saturday. But the unrest is reaching a boiling point and from the top down, elected officials are pressing for questions about the U.S. role in the assault to get a full airing on Capitol Hill next week. The coalition's involvement deepened after French fighter jets shot down a Libyan plane amid allegations Qaddafi's forces violated the no-fly zone.

Rep. Dennis Kucinich, D-Ohio, sent a letter to Obama Thursday announcing his intention to offer an amendment stripping the Libya operation of funding. Rep. Bruce Braley, D-Iowa, also wrote a letter asking Obama for a full accounting of the mission's costs.

"We must know how much a third military conflict will cost us," he wrote.

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Earlier, Senate Armed Services Committee Chairman Carl Levin, D-Mich., said a hearing scheduled for next week will probably focus on Libya. Sen. Richard Lugar, R-Ind., ranking Republican on the Senate Foreign Relations Committee, also said "prompt" hearings are "essential."

Not all lawmakers raising concerns about the U.S. military's involvement are opposed to the intervention. Levin, Sen. Dick Durbin, D-Ill., and Sen. Jack Reed, D-R.I., all backed the president on a conference call Wednesday. House Speaker John Boehner also has said the United States has a "moral obligation" to help those standing up to Qaddafi.

Rather, the principal complaint on Capitol Hill is that the administration has not engaged Congress to the degree it has engaged international partners.

Durbin made clear he would support a congressional vote on Libya -- though a defense source told Fox News there are no plans to seek permission from Congress. And Boehner sent a lengthy letter to the president Wednesday complaining that the administration has kept Congress out of the loop. He said members of the House remain concerned that the administration has not outlined a clear mission, given that its stated policy is to get rid of Qaddafi but the military strikes are not considered part of that.

"Because of the conflicting messages from the administration and our coalition partners, there is a lack of clarity over the objectives of this mission, what our national security interests are, and how it fits into our overarching policy for the Middle East. The American people deserve answers to these questions," Boehner wrote, adding that "it is regrettable that no opportunity was afforded to consult with congressional leaders."

Boehner also called the conflict "war," a term administration officials have studiously avoided. The administration describes the U.S. role as limited and insists the military will soon hand over command to an international coalition responsible for maintaining the no-fly zone. Officials say the president is well within his constitutional right.

Denis McDonough, deputy national security adviser, suggested in an interview on PBS that time was a factor in the decision to authorize the strikes without a lengthy debate.

"We have been talking with Congress about this now for a couple weeks. But the bottom line is, we had an opportunity to move after we had brought the international community along with us last Thursday night in that U.N. Security Council resolution," he said. "We had an opportunity to move with alacrity and speed and agility, as our armed forces always do, and protected Benghazi."

The strikes appear to have at least slowed Qaddafi's momentum against rebel forces.

House Minority Leader Nancy Pelosi, D-Calif., gave her full support to the president's actions.

"Actions taken by the international community have already prevented Qaddafi from implementing his threat to 'show no mercy' to his own people," she said. "U.S. participation is strengthened by the president's continued consultation with Congress."

But some lawmakers say the president has stepped way beyond his authority.

"The United States cannot afford, nor do we have the authority, to intervene," said Kucinich.

Rep. Tom McClintock, R-Calif., sent a letter to the president Wednesday calling his actions "unconstitutional."

Noting that the Constitution vests Congress with the authority to declare war, he said the president's prior letter to Congress "fails to explain how a resolution of the United Nations Security Council is necessary to commit this nation to war but that an act of Congress is not."