President Barack Obama continues to rally support for his plan to punish Syria for using chemical weapons against its own people, and several senators may be crucial to getting the 60 votes needed to move forward on a use of force resolution.

Not every member on this list will be a “yes” — indeed, some most definitely will vote “no” — but each senator can influence the debate as the United States considers potential military engagement in another Middle Eastern country.

On Monday, the Syrian government indicated it may be willing to give up its chemical weapons to avoid a strike, but that doesn’t get these senators off the hook for a vote as early as this week. White House spokesman Jay Carney told reporters that the only reason the Syrians were even floating the idea is because of the threat of a strike.

“We need to keep the pressure on,” Carney said. “The only reason why we are seeing this proposal is because of the U.S. threat of military action.”

Majority Leader Harry Reid opened the Senate Monday by noting the importance of the debate to come. “This matter demands the attention of the Senate and this country,” the Nevada Democrat said. “Regardless of where senators stand on the merits of this issue, all should agree that we should have this debate.”

Reid noted that the week will be filled with personal appeals and classified briefings from senior administration officials, including Obama himself. The president is due to address the Senate Democrats’ weekly lunch on Tuesday and has extended an offer to speak to GOP senators as well, Reid said.

Before Monday’s development, some senators had already been privately wined-and-dined by Vice President Joseph R. Biden Jr. and Obama, while others have visited the White House or been on the receiving end of a call from the president.

But there are some senators who are worth watching more closely than others as the debate unfolds this week.

Senate Minority Leader Mitch McConnell, R-Ky.: McConnell has been relatively quiet on Syria and is in a tough spot politically. He is a congressional leader who typically would support such action. But he also faces a tough re-election bid and a conservative challenger in a state where libertarian, non-interventionist Sen. Rand Paul has become more of a driver of the political narrative than he is.

Sen. John Cornyn, R-Texas: As the No. 2 Senate Republican, Cornyn is in much the same straits as McConnell. But instead of Rand Paul, his home-state tea party darling, Sen. Ted Cruz, has been drumming up anti-strike fervor, a situation that could cause political headaches for Cornyn if the two are on opposite sides.

Sen. Rand Paul, R-Ky.: Paul is definitely a “no” on the resolution to authorize force in Syria; the question is how much noise will he make between now and a final vote. He could force leaders to use the maximum amount of debate time by staging a filibuster that needs to be cut off. He might also pressure other GOP colleagues who ordinarily might have supported engagement in Syria to oppose it for fear of political retribution from the right. On Monday, he sent a “Dear Colleague” letter to senators urging them to vote “no.”

Sens. Joe Manchin III, D-W.Va./Heidi Heitkamp, D-N.D.: Manchin has demonstrated a near-compulsive need to insert himself into this Congress’ more significant debates, with a mixed record of success (a loss on background checks; a win on student loans).

On Syria, he and Heitkamp have floated a resolution that, as we previously reported, seemed at first to have no natural constituency. But now that the Syrians appear to be willing to surrender their chemical weapons to an international authority, the Democratic senators’ proposal seems almost prescient. The Manchin-Heitkamp plan would give the Syrian regime 45 days to sign on to the Chemical Weapons Convention and take “concrete steps” to comply. If the Syrians didn’t comply, the U.S. would be permitted to consider unspecified retribution.

A source tracking the resolution said Manchin and Heitkamp have been assured a vote on their plan, but leadership sources would not confirm that.

Sen. Richard J. Durbin, D-Ill.: Durbin is the No. 2 Senate Democrat, an ally of Obama, a previous opponent to wars and a supporter of human rights. He’s also now the guy who controls the giant defense spending bill. He backed the Senate Foreign Relations language out of committee, but as we reported earlier, he made a careful effort to reconcile his past positions with his current ones.

Sen. Bob Corker, R-Tenn.: Relatively new to the foreign affairs game, Corker has been boosting his public profile on the issue as the new top Republican on the Foreign Relations Committee. But Syria will be the first real test of his internal clout on an important issue. A GOP aide told us two weeks ago that Corker’s influence on international affairs was “growing.” Yet the current Republican Conference is difficult to navigate, and with Paul or Cruz speaking loudly on Syria, it’s unclear which voices will rise above the dissent.

Sen. John McCain, R-Ariz.: There is a certain power in having strong positions and no reservations about using multiple platforms to express them. McCain is the unofficial leader of the Senate’s hawks. He and other supporters of a military strike are looking for a stronger U.S. response to the Syrian regime’s alleged use of chemical weapons than the administration is currently contemplating.

Sen. Kelly Ayotte, R-N.H.: Ayotte was one of a handful of senators who dined with Biden at the Naval Observatory on Sunday night. She had not yet decided how she would vote at the time of publication, and a “no” certainly might jeopardize her tenuous place as the replacement for former Sen. Joseph I. Lieberman in McCain and Sen. Lindsey Graham’s inner circle of hawks. Ayotte fits a lot of interesting, and at times conflicting, profiles in addition to her association with McCain: She’s one of the last New England Republicans and rode a tea party wave to Congress in 2010.

Sen. Jack Reed, D-R.I.: Reed is one of the smartest and most articulate members on foreign affairs that no one ever talks to. In line to take the Senate Armed Services Committee gavel when Sen. Carl Levin, D-Mich., retires next year, Reed was one of 23 senators to vote against authorizing force in Iraq in 2002. If he does say something on Syria, expect it to be thoughtful and nuanced.