"We don't have the guts to stand up and vote yes or no? We want to vote maybe? Tell that to the families in Newtown" and other communities where there have been mass shootings, said Senate Judiciary Committee Chairman Patrick Leahy, D-Vt.
But Sen. Ted Cruz, R-Texas, one of 13 conservative senators who want to block the debate, said the Senate bill puts "burdens on law abiding citizens exercising a constitutional right." He said none of its provisions "would have done anything to prevent the horrible tragedy of Sandy Hook."
Obama was calling senators from both parties Tuesday to push for the gun bill, according to a White House official.
Reid's determination to stage a vote came despite continued inconclusive talks between Sens. Joe Manchin, D-W.Va., and Patrick Toomey, R-Pa., aimed at finding compromise on expanding background checks to more gun purchasers. Such a compromise would be likely to attract bipartisan support because both lawmakers are among their parties' most conservative members.
The checks, aimed at keeping firearms from criminals and certain other buyers, are the cornerstone of Obama's gun plan, which has been struggling in Congress. Democrats have been buoyed by polls consistently showing more than 8 in 10 Americans support subjecting more buyers to background checks.
A Senate vote to begin debating the guns package would mark a temporary victory for Obama and his allies.
But some Republicans, though eager to avoid blocking debate on the plan, could well vote against the measure on final passage. Coupled with resistance by leaders of the GOP-run House to main parts of Obama's effort including bans on assault weapons and high-capacity ammunition magazines the ultimate outcome seems shaky for the Democrats.
Reid said he did not know if he had the 60 votes he will need to defeat the conservatives' roadblock. But at least seven Republicans have said they want to begin debate or have indicated a willingness to consider it: Sens. John McCain of Arizona, Lindsey Graham of South Carolina, Tom Coburn of Oklahoma, Johnny Isakson of Georgia, Susan Collins of Maine, Roy Blunt of Missouri and Mark Kirk of Illinois.
But some moderate Democrats are remaining noncommittal and might oppose opening the gun debate, including Sens. Mark Begich of Alaska and Mark Pryor of Arkansas, who are seeking re-election next year.
Begich declined to directly state his position and said of Alaskans, "We like our guns."
There are 53 Senate Democrats and two independents who lean Democratic.
In a written statement, Sen. Mike Lee, R-Utah, said conservatives want to prevent Obama from rushing the legislation through Congress "because he knows that as Americans begin to find out what is in the bill, they will oppose it."
Senate Minority Leader Mitch McConnell, R-Ky., has said he will join the conservatives in their attempt to block debate.
The bill would expand required federal background checks to nearly all gun transactions, stiffen penalties for illegal firearms trafficking and provide a small boost in school safety aid.
Eleven Sandy Hook family members representing eight of the shooting victims were on Capitol Hill to lobby senators from both parties for gun legislation, including Isakson.
"We bring a face to this tragedy," said Mark Barden, who lost his 7-year-old son, Daniel. "We bring a very personal perspective. People should listen to what we have to say and move the debate forward. It's not just about our tragedy. Lots of kids are killed every day in this nation. We have to help lead the change."
Some of the relatives had breakfast with Vice President Joe Biden at his residence in the Naval Observatory. Later in the day, Biden spoke to law enforcement officials at the White House and told reporters that conservatives would not succeed in blocking debate.
"This is not one of these votes that they block a vote and somehow we're going to go away," Biden said. "The American public will not stand for it."
The president's gun-control proposals have hit opposition from the National Rifle Association, which was using the Internet and emails to urge its members it claims nearly 5 million to tell members of Congress of their opposition.
In GOP-heavy Louisiana, where Democratic Sen. Mary Landrieu is seeking re-election next year, the NRA wrote to its members, "Please contact Senator Landrieu and encourage her to oppose this anti-freedom legislation."
Counteracting that has been an effort by Mayors Against Illegal Guns, one of whose leaders is billionaire New York City Mayor Michael Bloomberg.
The group was running a television ad in Pennsylvania asking voters to contact Toomey and tell him to back expanded background checks. It also said it will keep track of key gun-related congressional roll calls and make the information available to voters and contributors a tactic long used by the NRA and other groups.
Manchin has been hoping for a deal with Toomey that would expand the requirement to sales at gun shows and online while exempting other transactions, such as those between relatives and those involving private, face-to-face purchases.
Currently, federal background checks are required for sales by licensed gun dealers but not for other transactions.