US Democrats demanded a vote on a gun bill and called on Republicans to stop threatening to block it, as families of the victims of last year's deadly shooting in Newtown arrived in Washington to lobby Congress for stricter gun control measures.

On Tuesday, Senate majority leader Harry Reid said the American people deserve a debate on the legislation.

He said he was shocked that 13 conservative senators had lined up to block the debate, and promised to overcome the procedural tactic, known as a filibuster, with a vote on Thursday.

Also on Tuesday, family members of the Newtown school shooting victims flew into Washington to press for gun-control legislation. They kept a low profile as they held private meetings with US senators.

The gun legislation will need 60 votes to break the Republican filibuster. Democrats control only 55 Senate votes, meaning Republican support will be needed to move to debate and a vote on passage.

"We need to move to this legislation," Reid told reporters, weeks after the judiciary committee approved a three-part bill calling for background checks for all gun sales, felony penalties for gun trafficking, and new funding to boost school safety.

"It would be a real slap in the face to the American people not to do something on background checks, on school safety, on federal trafficking, which everybody thinks is a good idea," he said.

Republican threat

Republican leader Mitch McConnell said he and his fellow conservatives would press ahead with the filibuster. "The one [Reid] indicated he was going to try to move to clearly has no bipartisan support," he said.

But at least 10 Senate Republicans have told reporters they would like to have an open debate and vote on gun legislation.

Reid has said he would allow senators to offer various amendments to improve the bill, a gesture that led Republicans like Lindsey Graham to support allowing a vote.

"If your goal is to have a process that allows people to read it, understand it, debate it, amend it and vote on it, count me in," Graham said.

Republican senator John McCain of Arizona criticised the effort to block the bill and called on his fellow Republicans to allow a full debate.

"It's incomprehensible to me that we would not move forward with debate and amendments on an issue this important to the American people," McCain told reporters.

Obama push

This week's effort coincided with president Barack Obama's eleventh-hour appeal to Congress to allow a vote.

Obama heaped on pressure with phone calls to Republican and Democratic senators Tuesday to discuss measures to prevent gun violence, according to a White House official.

Obama faces resistance from Republicans in conservative-leaning states where support for gun ownership is widespread, and where efforts to crack down on gun violence are seen by many voters as infringing on the constitutional right to bear arms.

Meanwhile, vice president Joe Biden warned that the world would be mystified if Republicans followed through on the filibuster threat.

"It appears that now not only are some of the senators not willing to stand and be counted, they're prepared to stop anybody from being able to be counted. I mean, it's almost mind-boggling," he said.