"I believe that we will get there," the committee's chairman, Democratic Senator Robert Menendez, said when asked if the Senate had the 60 votes needed to pass the resolution.
But, he added, "I think our resolution that we will ultimately see will be far more tailored than what the administration sent us."
"At the end of the day, (it) will strike the balance between the need to act and act in a way that meets our goals and not create an open-ended, boots-on-the-ground long-term proposition," he told CNBC in the interview.
U.S. Secretary of State John Kerry and Secretary of Defense Chuck Hagel will present the Obama administration's case for U.S. military action at the hearing, which is set to begin at 2:30 p.m. ET (1830 GMT).
The congressional panel comes after President Barack Obama said on Saturday he would seek lawmakers' approval for a possible strike in response to what Washington says was a sarin gas attack by the Syrian government that killed more than 1,400 people, many of them children, near Damascus on Aug. 21.
While saying he would seek such approval, Obama has said he does not require congressional authorization for a strike on Syria, which has blamed the attack on rebel forces.
Some U.S. lawmakers, including Obama's fellow Democrats, have said they are concerned that the president's draft could be too open-ended and allow possible use of ground troops or eventual attacks on other countries.
Menendez, speaking on CBS News, said he wants Kerry and Hagel to offer "the full case for the use of force" and detail "what that campaign will look like in broad terms, especially as it relates to the end result."
"If those two streams of information come forcefully before the committee, I think the committee will act to ultimately pursue the use of force and a resolution and then work its way to the floor of the Senate," he told the CBS show, "This Morning."
The committee will also hold an closed hearing on Wednesday to discuss the intelligence related to Syria, Menendez told CBS.
It could then begin debate on a Senate version of the bill on Wednesday afternoon, with the aim of sending it to the full Senate for debate next week.
The House of Representatives and the Senate return from their summer recess on Sept. 9. Both chambers would have to approve the authorization, and it remains unclear whether the Obama administration has the votes.
Republican Senator John McCain, who attended a White House meeting on Syria on Monday, said Obama "would seriously consider" providing weapons to opponents fighting Syrian President Bashar al-Assad.
"We discussed ... increasing the capabilities and that means providing not only weapons, but the kind of weapons they need, which are anti-armor and anti-air. AK-47s don't do very well against tanks," McCain, a member of the committee, told CNN's "New Day."
Both McCain and Menendez said that although any action would be aimed at degrading Assad's capabilities to deliver chemical weapons it could also undermine the Syrian government itself and shift momentum in favor of the rebels.
But Senator Ron Johnson, a Republican member of the committee, said he was concerned that Obama might take action that was ineffective and which ultimately made matters worse.
"We've got to see the entire strategy. I've got to see that there's a long-term commitment to follow through on whatever the blowback might be of his actions," he told MSNBC's "The Daily Rundown." (Reporting by Susan Heavey; additional reporting by Vicki Allen; Editing by David Brunnstrom)