Senate Majority Leader Harry Reid said Monday that he'll schedule a critical test vote for Wednesday on a resolution authorizing President Obama to launch a military strike against the Syrian government in retaliation for its chemical weapons use.

Reid, D-Nev., who supports the resolution, argued strenuously in a floor speech that senators should provide the 60 votes needed to advance the measure.

He compared Syria's use of chemical weapons to the gassing of Jews during World War II in Nazi-run concentration camps. At the time, Reid noted, some countries decided to remain neutral rather than come to the aide of the Jews.

"Bergen-Belsen, Treblinka, Auschwitz — never again, swore the world, never again would we permit these poisonous weapons of war," Reid said. "Now we are faced with that choice again."

Reid made reference to the United States Holocaust Memorial Museum, located blocks from the Capitol and a plaque in the museum from Dante's "Inferno" that reads, "The hottest places in hell are reserved for those who, in times of great moral crisis, maintain their neutrality."

Reid said he's "thought about those words very often … as I've considered whether America should take action to prevent further atrocities in Syria."

Opposition to the resolution, however, is mounting among both Democrats and Republicans, with Sens. Heidi Heitkamp, D-N.D., and Lamar Alexander, R-Tenn., among the latest to announce that they'll vote against it.

Sen. Dan Coats, R-Ind., said he also will vote no after hearing from constituents.

"The vast majority, shocking majority, of Hoosiers I have heard from are opposed to U.S. engagement in Syria," Coats said.

Obama will meet privately with Democrats in a rare Capitol Hill visit on Tuesday to lobby on behalf of the resolution. He'll meet privately with Republicans on Tuesday before making a prime-time address to the nation.

"After calling the White House today, we learned that the president would like to attend the Senate GOP lunch [Tuesday] to discuss the Syria resolution," a spokesman for Senate Minority Leader Mitch McConnell, R-Ky., said. "He is welcome to join the lunch, and we are told that he will in fact attend."

Sen. Bill Nelson, D-Fla., is one of only a handful of Democrats who has publicly declared support for the resolution.

"If we vote no, where does that leave the president on any kind of negotiations in the future?" Nelson said on the Senate floor Monday afternoon.