Senate Minority Leader Mitch McConnell (R-Ky.) on Tuesday did not offer support for a military strike against Syria.

In a stark contrast with GOP leaders in the House, McConnell voiced skepticism about a strike and said Obama needed to explain more to Congress and the public.

{mosads}“While we are learning more about his plans, Congress and our constituents would all benefit from knowing more about what it is he thinks needs to be done — and can be accomplished — in Syria and the region,” McConnell said in a statement after meeting with Obama at the White House.

McConnell is up for reelection in 2014 and is facing a tough Tea Party challenge from the right. 

Fellow Kentucky GOP Sen. Rand Paul opposes military intervention in Syria, something that may be weighing on McConnell.

Senate Republicans said the president needs to do a better job explaining his rationale for a military strike in the wake of chemical weapons attacks outside of Damascus.

The GOP skepticism means that Senate Majority Leader Harry Reid (D-Nev.) will have to rely heavily on his own caucus to pass a resolution authorizing force.

This could force him to corral skeptical liberals like Sen. Chris Murphy (D-Conn.), who have expressed concern about another military action in the Middle East.

McConnell’s deputy, Senate Republican Whip John Cornyn (Texas), also voiced misgivings about a limited strike against the military forces of Syrian President Bashar al-Assad. 

 “What the president can do is to make the case to the American people. It’s important that he bring Congress in but he needs to make the case to the American people and that case hasn’t been made yet,” Cornyn told reporters.

Cornyn said a limited military strike might have a counterproductive effect.

“If it is so targeted and so limited it may have the opposite effect than the president intends,” he said. “It may be viewed as so insignificant that it actually emboldens other international bullies.”

Sen. Jim Risch (R-Idaho), a member of the Senate Foreign Relations Committee, said he was “extremely reluctant” to authorize a strike on Libya.

But Sen. Bob Corker (Tenn.), the top ranking Republican on the Foreign Relations panel, predicted enough Republicans would support an authorization resolution to pass it through the Senate with at least 60 votes.

Corker said Obama needs to make a broader argument for why it is important to support rebel fighters in Syria and why the conflict is important to U.S. national security.

“I have a strong sense that we will be able to come to terms fairly quickly with what an authorization ought to say,” Corker said of his talks with Senate Democratic leaders over an authorization of force resolution.

This story was updated at 1:58 p.m.