Washington (CNN) -- When U.S. President Barack Obama said Monday it would be wrong to seek regime change in Libya by force, Republican lawmakers took issue -- saying removing Libyan leader Moammar Gadhafi is and should be precisely the goal.
Gadhafi must have been comforted to hear the president's words, Sen. John McCain, R-Arizona, said following Obama's televised address.
"If we tell Gadhafi, 'Don't worry, you won't be removed by force,' I think that's very encouraging to Gadhafi," McCain said, after Obama delivered a speech explaining U.S. intervention in Libya.
McCain said the president's words were "puzzling" because Obama has previously said that U.S. policy is for Gadhafi's ouster.
"The reason why we wage wars is to achieve the results of a policy that we state," McCain said.
Sen. Lindsey Graham, R-South Carolina, agreed with McCain, his felllow member of the Senate Armed Services Committee.
"The goal of this country is to replace Gadhafi," Graham told CNN.
Overall, however, McCain said Obama made a "strong case" for the military effort in Libya and laid out the reasons why the president thought it was important to intervene.
Democrat Bill Richardson, a former governor of New Mexico who served as the U.S. ambassador to the United Nations, said he was satisfied with the speech.
Richardson told CNN that Obama said the purpose of the military mission is to avert a humanitarian disaster, to protect civilian lives, and to prevent a refugee crisis in neighboring Tunisia and Egypt.
He said Obama probably should have called more members of Congress before deciding to join the military effort, but he pointed out this is not a war but a limited military engagement.
"He explained the objective and he explained what he wants to do," Richardson said.
Republicans disagreed. Sen. Olympia Snowe, R-Maine, a senior member of the Senate Select Committee of Intelligence, and Rep. Ileana Ros-Lehtinen, R-Florida, both said the president failed to explain the extent of U.S. involvement and when that will end.
House Speaker John Boehner, R-Ohio, also said the president's speech failed to provide much clarity.
"Nine days into this military intervention, Americans still have no answer to the fundamental question: What does success in Libya look like?" said Boehner spokesman Michael Steel.
Boehner sent a letter to Obama last week in which he asked specific questions about the Libya mission, including whether the U.S. military would take on a larger role if the coalition fell apart.
The House speaker also complained that the nine days it took for Obama to lay out the reasons for U.S. involvement was "a long time," according to Steel.
Former New York Mayor Rudy Giuliani, a former Republican presidential candidate, said Obama's speech didn't just fail to clarify the mission but "made things even murkier than they were before."
"The president says our mission is to protect the people of Libya," Giuliani said. "Well, how do you protect the people of Libya and not be for regime change in Libya? Isn't the danger for the people of Libya Gadhafi?"
He added, "The president of the United States did not define a clear goal. He didn't tell us what success is. He can't, because he's contradicting himself. You know what success is? Success is removing Gadhafi. He just doesn't want to say that."
Republican Sen. Rand Paul of Kentucky, a Tea Party favorite and possible 2012 presidential contender, said intervening in Libya is not in the national interest.
In a response to the speech, posted on YouTube, the freshman senator asked, "What imminent threat did Ghadafi or Libya pose to the United States?"
Rep. Emanuel Cleaver, D-Missouri, the chairman of the Congressional Black Caucus, said he was pleased with the president's announcement that the United States will transfer command of the mission to NATO on Wednesday, and that the United States will take a supporting role in the effort.
"We cannot afford another Iraq or Afghanistan, and I firmly believe that the president fully understands that," he said.
Cleaver added he doesn't personally support the military engagement in Libya but understands Obama acted to prevent a "potential genocide" in the country.
One congressman, Rep. Bruce Braley, D-Iowa, pointed out Obama made no mention of the cost of the mission, which both Democrats and Republicans have sought.
Braley sent a letter to Obama last week asking for a full accounting of the Libyan conflict and the pricetag and said the president's speech Monday night provided no answers.
"I'm concerned, and I know many Americans are concerned, that tonight we didn't get a clear and accurate accounting from the president on how much this conflict in Libya is going to cost American taxpayers," Braley said in a statement after the speech. "We've got two wars in Iraq and Afghanistan, and Americans deserve to hear from our president what this third conflict is going to cost us."
Braley said he plans to meet with Defense Secretary Robert Gates and Secretary of State Hillary Clinton later this week and will press them on both the costs of the mission and "their strategy for moving forward in Libya."
The United States has already fired close to 200 Tomahawk missiles in Libya. The cost of that alone is between $250 million and $300 million. By some estimates, it costs about $10,000 an hour to keep a U.S. fighter jet in the air, and U.S. jets have flown nearly 1,000 sorties, many of which last five or six hours.
Some have estimated the costs of the Libya mission could reach $1 billion.
Sen. Richard Lugar, R-Indiana, has also called for a full accounting of the costs.
Graham took issue with those seeking clarification on the costs of the mission, saying the cost of not acting -- "instability forever" and large spikes in the price of oil for both the United States and its allies -- is far greater.
CNN's Dana Bash, Deirdre Walsh, and Chris Lawrence contributed to this report