Sens. Tom Udall (D-N.M), Chris Murphy (D-Conn.), Mike Lee (R-Utah), and Rand Paul (R-Ky.) have introduced legislation that would block military funds from going to Syria.
Text of the bill below, courtesy of Sen. Udall's office:
Title: To restrict funds related to escalating United States military involvement in Syria. 
Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled,
SECTION 1. SHORT TITLE.
This Act may be cited as the “Protecting Americans from the Proliferation of Weapons to Terrorists Act of 2013”. 
SEC. 2. PROHIBITION ON FUNDS TO ESCALATE UNITED STATES MILITARY INVOLVEMENT IN SYRIA.
(a) In General.—Except as provided under subsection (b), no funds made available to the Central Intelligence Agency, the Department of Defense, or any other agency or entity of the United States involved in intelligence activities may be obligated or expended for the purpose of, or in a manner which would have the effect of, supporting, directly or indirectly, military or paramilitary operations in Syria by any nation, group, organization, movement, or individual.
(b) Exception.—The prohibition under subsection (a) does not apply to funds obligated for non-lethal humanitarian assistance for the Syrian people provided directly by the United States Government, through nongovernmental organizations and contractors, or through foreign governments. 
(c) Duration of Prohibition.—The prohibition under subsection (a) shall cease to apply only if a joint resolution approving assistance for military or paramilitary operations in Syria is enacted.
(d) Quarterly Reports.—Not later than 90 days after the date of the enactment of this Act, and every 90 days thereafter, the Secretary of State shall submit to Congress a report on assistance provided to groups, organizations, movements, and individuals in Syria. 
(e) Non-lethal Humanitarian Assistance Defined.—In this Act, the term “non-lethal humanitarian assistance” means humanitarian assistance that is not weapons, ammunition, or other equipment or material that is designed to inflict serious bodily harm or death.
Assad’s opposition includes jihadists who are increasingly sideliningmoderate rebels in Syria. Groups like Jabhat al-Nusra have connections to Al Qaeda and are hoping to establish an Islamic caliphate. While those who argue for intervention say that groups like Jabhat al-Nusra will not get their hands on whatever weapons the U.S. and other western nations send to rebels in Syria there is no way that this can be guaranteed.
Thankfully, there are at least four Senators who seem to realize that sending weapons to a region where Assad’s regime (with support from Iran, Russia, and Hezbollah) is fighting jihadist rebels as well as other opposition groups in a conflict that could overspill into Syria’s neighbors is not a good idea.
UPDATE: Looks like Sen. Ted Cruz (R-Texas) thinks the U.S. should locate Assad's chemical weapons, destroy them, and "get out."