The scant support virtually assures rejection of the bill, a centerpiece of Obama's bid to curb gun violence in wake of a massacre at a Connecticut elementary school on December 14 that left 20 children and six adults dead.
"Right now," Reid told reporters, the bill drafted by Democratic Senator Dianne Feinstein of California, "has less than 40 votes."
A simple majority would be needed to win passage of the bill in the Democratic-led Senate, but 60 would likely be required to first clear an anticipated Republican procedural roadblock.
Obama, Feinstein and others backers of the bill to renew a ban against the sale and manufacture of military-style assault weapons, argue that the firearms should be removed from the street.
But opponents, a number of Senate Republicans, along with some Democrats from rural areas where guns are popular, argue that the action would amount to a violation of the right to bear arms, which is enshrined in the US Constitution.
