In a private meeting at the White House on Monday with Sen. John McCain, President Obama said he plans to give Syrian rebels more advanced weapons, according to McCain. If this happens, it would mark an expansion of Obama’s latest Syria strategy of possibly mounting a military response to Bashar al-Assad’s use of chemical weapons.

McCain and Sen. Lindsey Graham met with Obama to discuss the plan, which, as currently outlined by the White House, involves a limited mission to punish the Syrian regime’s use of chemical weapons, as the Syrian president did most recently on August 21, and deter future assaults. Administration officials have made clear that “regime change” is not an objective of the mission. But Obama’s new arming strategy would certainly help the rebels, whose goal is removal of the Assad regime. The White House didn’t respond to requests for comment Monday.

“He said that he was willing to upgrade the capabilities of the Free Syrian Army,” McCain said in an interview with The Daily Beast, referring to the largest of the rebel groups. “This was a shift in the president’s thought and actions from before.”

McCain and Graham have said they want to know the president’s broader strategy for the Syrian conflict before voting on the war authorization.

Obama didn’t say which weapons he would give the rebels, but McCain said the Free Syrian Army needs antiarmor and antiaircraft weapons to shift the momentum on the ground to its side. He said if the administration gives him enough specifics about the new arms pledges, he’ll vote to authorize military action.

“For the first time we have an outline of action that could lead to the removal of Bashar al-Assad,” McCain said. “I’m certainly willing to join in that effort, but I need to know a lot of the details.”

Previous weapons pledges by Obama to the Syrian rebels have not been honored, McCain said. In June the White House promised to increase its military assistance to the FSA in response to another set of chemical-weapons attacks that the U.S. intelligence community concluded had been perpetrated by the Syrian regime in March. But those weapons never arrived, so lawmakers need greater assurances this time around, McCain said.

“As of right now, they haven’t received one weapon from the United States. Reports are that the United States has constrained other countries from giving them the kinds of things they need,” said McCain. “In order for me to be convinced about this, we need to know how they are going to do it [before we vote].”

McCain will press administration officials for those details at a Tuesday hearing of the Senate Foreign Relations Committee at which Secretary of State John Kerry, Defense Secretary Chuck Hagel, and Joint Chiefs of Staff chairman Gen. Martin Dempsey all are scheduled to speak.

The hearing kicks off what is sure to be a difficult task for Obama and his team in Congress as they make the case to lawmakers to authorize the use of force in Syria.

Classified briefings on Capitol Hill have stressed evidence that Assad’s military was responsible for a series of sarin-gas attacks August 21 on several Damascus suburbs and the importance of enforcing a red line in response. One problem with any U.S. retaliation, however, is that chemical-weapons depots are scattered throughout the country, often in and around civilian areas, creating the risk of an unintended chemical-weapons discharge if attacked. That’s why the current war plans don’t include targeting the stockpiles of chemical weapons, precursor chemicals, or transit points for the chemicals, according to three U.S. lawmakers who attended the briefings.

Also, many of the weapons have been mobilized, and in some cases the U.S. hasn’t been able to keep track of them. Dempsey said in April that he could not guarantee that the U.S. had the capabilities to secure Syria’s chemical-weapons stockpiles.

Sen. Bob Corker, the ranking Republican on the Senate Foreign Relations Committee, told The Daily Beast Monday that he thinks trying to degrade the actual weapons would not be successful.

“There are all kinds of facilities. You have some that have elements for mixing, and these are scattered throughout the country. Some are compounds that have a bigger significance ... Many are in areas near civilians,” he said.

Instead, lawmakers say, the war plan at this point is aimed at Assad’s capability to deliver the chemical weapons through his Air Force and supply of short-range rockets and missiles. “They don’t want to hit the chemical weapons, because they cannot destroy them,” one member of Congress told The Daily Beast. “The focus will be on command and control and delivery.”

Members of both parties are also aiming to limit what was seen as an overly broad resolution submitted by the White House on Saturday. On Sunday Corker and Sen. Patrick Leahy both said they were pressing to limit the resolution.

“I got a copy immediately when it was produced, and it’s broad. Because of where we’ve been with Iraq and Afghanistan, I just think it’s likely—more than likely—that the authorization at least on the Senate side will be more narrow,” Corker said.

Another member of the House who asked not to use his name said Democrats and Republicans have begun to express interest in limiting the duration of the military strikes and including language that expressly forbids sending American ground troops to Syria. McCain said attempts to limit the president’s authority in the resolution would be “harmful.”

Another concern for Republicans is how the White House intends to pay for military operations in Syria. Rep. Howard “Buck” McKeon, the chairman of the House Armed Services Committee, told CNN on Sunday that the president should also end the mandatory budget cuts to the military ironed out in the current budget deal known as sequestration before launching airstrikes on Syria.

“We cannot keep asking the military to perform mission after mission with sequestration and military cuts hanging over their heads,” he said. “We have to take care of our own people first.” One House staffer told The Daily Beast that rough estimates for the Syria campaign range between $500 million and $1 billion.