The Senate is to vote Wednesday afternoon on what could be the biggest change in U.S. gun laws in two decades.

Senators will take up the bipartisan proposal from Sens. Joe Manchin, D-W.Va., and Pat Toomey, R-Pa., to expand background checks on firearms purchases and close the so-called gun show loophole at 4 p.m., Politico reports.

But 60 votes are needed to break a filibuster threat and force a vote, and the White House and Democrats still lack the votes they need.

Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., reached a final agreement Tuesday evening setting up votes on eight additional amendments. They include Democratic proposals to ban assault weapons and high-capacity ammunition clips, a Republican proposal requiring states to honor other states' permits allowing concealed weapons, plus a broad GOP substitute for the whole measure.

Democrats, the White House and gun control groups were still lobbying undecided members Tuesday. Vice President Joe Biden has spoken with several senators on the issue. Majority Whip Richard Durbin, D-Ill., his party's chief vote counter, left a lunch of Democratic senators saying they would need support from nine or 10 Republicans -- a formidable task.

Among Republicans, only Toomey, Susan Collins of Maine and Mark Kirk of Illinois have committed to support the Senate proposal, Reuters reports. John McCain of Arizona said Sunday he was "favorably disposed" to it.

Several Democratic senators from states where hunting and guns are popular -- including Mark Pryor of Arkansas, Heidi Heitkamp of North Dakota, Mark Begich of Alaska and Mary Landrieu of Louisiana -- remain uncommitted.

Sens. Dean Heller, R-Nev., and Lisa Murkowksi, R-Alaska, came out against the bill Tuesday.

A Senate Democratic leadership aide told CBS News that even if the Manchin-Toomey bill fails, which seems likely, they could come back later with a new amendment on background checks, but the way forward after most of these amendments likely fail Wednesday is unclear.

Former Rep. Gabrielle Giffords, D-Ariz., who was nearly killed in the January 2011 Tuscon shooting, was on Capitol Hill on Tuesday to press for the Manchin-Toomey plan. Giffords received a long ovation when she entered the Senate Democratic Caucus luncheon with her husband, Mark Kelly.

“She’s our whip,” Manchin declared. But she did not speak herself.