WASHINGTON -- Relatives of victims of the Connecticut school shootings mounted a face-to-face lobbying effort Tuesday in hopes of turning around enough U.S. lawmakers to gain a Senate floor vote on meaningful gun restrictions as Senate Democrats approach a key decision on gun legislation.

Their effort follows President Barack Obama's remarks in Connecticut on Monday night on gun control, an issue catapulted into the national arena by December's gruesome slaying of 20 young children and six educators at the Sandy Hook Elementary School in Newtown, Connecticut.

"If you want the people you send to Washington to have just an iota of the courage that the educators at Sandy Hook showed when danger arrived on their doorstep, then we're all going to have to stand up," the president said.

Obama's proposals -- headlined by background checks for more gun buyers and bans on assault weapons and high-capacity ammunition magazines -- have hit opposition from the nation's powerful gun lobby, the National Rifle Association, and are struggling in Congress. Conservatives say they will use procedural tactics to try preventing the Senate from even debating firearms restrictions.

On Tuesday, Senate Majority Leader Harry Reid criticized Republicans anew for trying to prevent a gun debate, a move that will take a hard-to-achieve 60 votes to overcome in the 100-member chamber. Reid stood on the Senate floor before a poster-sized photo of a white picket fence with 26 slats, each bearing the name of one of the Newtown victims.

"We have a responsibility to safeguard these little kids," said Reid, a Democrat. "And unless we do something more than what's the law today, we have failed."

In a hopeful sign for Democrats, at least five Republican senators have indicated a willingness to oppose the conservatives' efforts to block the gun debate.

Sixty votes will be needed to head off the conservative stalling tactics in the 100-member chamber. There are 53 Democrats and two Democratic-leaning independents, though it remains unclear whether any moderate Democrats from Republican-leaning states might support the conservative effort.

"The American people ought to see where everybody stands on this," said Sen. Tom Coburn, a Republican who said he wants the debate to proceed. Expressing similar sentiments have been Republican Sens. John McCain, Lindsey Graham, Susan Collins and Johnny Isakson.

In a written statement, Sen. Mike Lee, a Republican leader of the effort to block the gun debate, said that effort would 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."

Underscoring the high emotional stakes, some Newtown families are in the halls of Congress lobbying senators to support gun restrictions, including 11 relatives Obama ferried back to Washington on aboard Air Force One after his speech.

The administration was continuing its efforts to pressure Republicans, with Vice-President Joe Biden and Attorney General Eric Holder making remarks Tuesday at the White House, joined by law enforcement officials.

Senate Democrats, meanwhile, are approaching decision time on whether they should try to get Republican support for expanding background checks for firearms sales or will follow the shakier path of pursuing the cornerstone of Obama's gun control effort on their own.

Democrats were holding a lunchtime meeting Tuesday to assess whether to seek a compromise with Republicans or try the shakier path of trying to advance a gun control bill over opposition objections.

Party leaders were giving Democratic Sen. Joe Manchin until later Tuesday to complete the talks with Republican Sen. Pat Toomey and see if they could reach an acceptable compromise.

An agreement between the two senators, both among the more conservative members of their parties, would boost efforts to expand background checks because it could attract bipartisan support. Abandoning those negotiations would put Democrats in a difficult position, making it hard for them to push a measure through the Senate and severely damaging Obama's gun control drive.

Further underscoring the tough road ahead for the Obama-backed legislation, a spokesman for Republican Senate Minority Leader Mitch McConnell said that he would join the effort to block debate on the legislation if Reid tries to bring the measure to the floor.

The conservative senators said the Democratic measure would violate the Second Amendment of the U.S. Constitution which guarantees the right to bear arms, citing "history's lesson that government cannot be in all places at all times, and history's warning about the oppression of a government that tries."