Their effort follows President Barack Obama's remarks in Hartford on gun control, an issue catapulted into the national arena by December's gruesome slaying of 20 first-graders and six educators in Newtown, Conn.
"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 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.
Underscoring the high emotional stakes, some Newtown families are in the Capitol lobbying senators to support gun restrictions, including 11 relatives Obama ferried back to Washington on Monday 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 Sen. Joe Manchin, D-W.Va., had reached an acceptable compromise - or had a realistic chance of getting one - with Sen. Pat Toomey, R-Pa. Party leaders were giving Manchin until later Tuesday to complete the talks, and a decision by Democrats seemed likely in the next couple of days.
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.
In a preview of the Senate's debate, 13 conservative Republicans delivered a letter Monday to Senate Majority Leader Harry Reid, D-Nev. They promised to try blocking lawmakers from beginning to consider the measure, a procedural move that takes 60 votes to curtail, a difficult hurdle in the 100-member chamber.
The conservatives, who included Sen. Mike Lee, R-Utah, said the Democratic effort would violate the Second Amendment 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."
"Shame on them," Reid responded as he brought Democratic gun legislation to the Senate floor, though debate did not formally begin.
"The least Republicans owe the parents of those 20 little babies who were murdered at Sandy Hook is a thoughtful debate about whether stronger laws could have saved their little girls and boys," Reid said.
Georgia's Sen. Johnny Isakson, a conservative Republican, said Tuesday on "CBS This Morning" that "the issue on background checks is how far they go and whether they violate rights of privacy." But he also said he believes the issue "deserves a vote up or down" in the Senate.
Reid could try beginning Senate debate on legislation that has already been approved by the Judiciary Committee. It would extend the background check requirement to nearly all gun purchases, strengthen laws against illegal firearms purchases and modestly boost aid for school safety.
If Reid does that, Senate Minority Leader Mitch McConnell, R-Ky., will join conservatives' efforts to prevent the measure from being debated, McConnell spokesman Don Stewart said.
In hopes of enhancing the prospects for Senate approval, Reid has been hoping a bipartisan deal could be struck. There are 53 Senate Democrats and two independents who lean toward them, meaning GOP support ultimately will be needed to reach 60 votes to move ahead.
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. The system is aimed at preventing criminals, people with severe mental health problems and others from getting firearms.
Sen. Mark Kirk, R-Ill., has also continued working for a bipartisan deal. Kirk, though, is considered too moderate to bring other GOP senators with him.
Efforts by Sen. Chuck Schumer, D-N.Y., to reach a background check compromise with conservative Sen. Tom Coburn, R-Okla., foundered over Schumer's insistence that records of private transactions be kept. Schumer said records are the only way to assure the checks were actually performed, while Coburn opposed them as a step toward government files on gun owners.