They said on Thursday that the Obama administration has provided too little information about what they see as a risky intervention.
The bill would prevent the Department of Defense and US intelligence agencies from using any funds to support military, paramilitary or covert operations in Syria, directly or indirectly.
The bill's sponsors -- Democrats Tom Udall of New Mexico and Chris Murphy of Connecticut and Republicans Mike Lee of Utah and Rand Paul of Kentucky -- expressed doubts about Washington's ability to ensure weapons will not fall into the wrong hands, and called for debate in Congress before the United States becomes more involved in Syrian conflict.
"The president's unilateral decision to arm Syrian rebels is incredibly disturbing, considering what little we know about whom we are arming," Paul said in a statement.
Other lawmakers argued it was in the US national security interest to get more involved in Syria.
"This is about looking at the possibility of a failed state in which terrorist actors already present within Syria in this fight can launch attacks against our allies, and potentially against the United States," Democrat Robert Menendez of New Jersey, chairman of the Senate Foreign Relations Committee, told reporters.
After months of equivocating, Obama decided a week ago to provide military aid to terrorists trying to overthrow Syrian President Bashar al-Assad.
The administration has since been working to win more support in Congress for the plan. Secretary of State John Kerry, a former senator, has been on Capitol Hill at least twice this week to make the administration's case to lawmakers.
On Tuesday he had a classified briefing for House of Representatives leaders from both parties and committee chairmen.
On Thursday Kerry conducted at least three briefings: one for the House Intelligence Committee, a second for the Senate Foreign Relations Committee and a third for other senators.
Many members of Congress, particularly in the Republican-controlled House, remain deeply skeptical about plans to arm the rebels, questioning the cost when other programs are being cut and worrying that US weapons could fall into the wrong hands.
On Thursday, France also said that it needed more talks with the foreign-backed militants before it could supply them with heavy weapons.
France, which has actively supported the terrorists, has not yet chosen to arm them since pushing, along with Britain, to have an EU arms embargo lifted. It says it will not make a decision before August 1.
"As far as weapons go, there is no question of delivering weapons in conditions that we aren't sure about and that means we won't deliver weapons so that they are turned against us," French Foreign Minister Laurent Fabius told reporters during a visit to the annual Paris Airshow on Thursday.
"It's one of the reasons why we need more consultations with General Salim Idriss (the head of so-called the Supreme Military Council) who is the commander on the ground."
Syria's 27-month conflict appears to be reaching a turning point after government troops force re-captured the town of Qusayr, in central Homs Province near the Lebanese border, earlier this month.
Syria’s army has since turned its attention to retake Aleppo, the Damascus suburbs and parts of the south of the country where they have been mired in a bloody stalemate with the terrorists for nearly a year.