U.S. President Barack Obama on Monday invited Republican Senators John McCain and Lindsey Graham to the White House to discuss military intervention in Syria as the administration is bracing for Congressional approval of strikes against Bashar al-Assad's government for punishing it for the alleged Aug. 21 use of chemical weapons on its citizens.

After the meeting with Obama, McCain warned against the peril of not backing up the president on an expressed threat to use force.

"If the Congress were to reject a resolution like this after the president of the United States has already committed to action, the consequences would be catastrophic," said McCain.

Obama announced Saturday that he would seek the authorization from Congress before taking military action to punish Assad's regime for the alleged Aug. 21 chemical weapons attack in the suburbs of Damascus, the Syrian capital, which reportedly killed at least 1,429 people, including 426 children. The Syrian government denied the accusation.

The White House on Saturday sent Congress a draft resolution to seek authority over a military strike against Syria in order to " deter, disrupt, prevent and degrade the potential" for future uses of chemical weapons or other weapons of mass destruction. It promised that the military action will be "limited" and will not involve sending U.S. troops to Syria.

As the first step of the "convince-path," senior officials on Sunday held a classified briefing with a group of ranking lawmakers, trying to convince them about the need for a military action against Syria, and to win their support in pending Congressional vote on the authorization.

The officials tried to convince the lawmakers why the U.S. government needs to respond to the Syrian crisis, in a push to garner more support to Obama's decision to launch a limited military strike on Syria.

The White House also dispatched Secretary of State John Kerry, Secretary of Defense Chuck Hagel, Chairman of the Joint Chiefs of Staff Martin Dempsey, National Security Advisor Susan Rice and National Intelligence Director James Clapper for a joint phone briefing with House Democrats as it is crucial to convince members of Obama's own party in order to garner the Congressional approval. Altogether 127 House Democrats dialed in for the 70-minute briefing.

Despite the White House's efforts, McCain said Sunday the administration still has a "long way to go" before securing the backing of lawmakers to use military force against Syria.

The main obstacle to the strike against Syria is a coalition built between liberal Democrats and libertarian Republicans, including Democratic Representatives Barbara Lee, Charles Rangel, Republican Senators Rand Paul, Marco Rubio, as well as Republican Representative Justin Amash.

Proponents to the strike included hawks such as McCain and Graham, who favored taking a step further than just missile attacks. Others in favor of strike also include Democratic leaders such as House Minority Leader Nancy Pelosi, House Minority Whip Steny Hoyer, Senate Foreign Relations Committee Chairman Robert Menendez and Senate Judiciary Committee Chairman Patrick Leahy. Senate Majority Leader Harry Reid and House Majority Leader Eric Cantor were seen as leaning toward intervention.

Republican leadership seems more vague on their position. Senate Minority leader Mitch McConnell and House Speaker John Boehner haven't publicly expressed their thoughts.

Obama is also scheduled to meet Tuesday with leaders of the Senate and House's Armed Services Committee, Foreign Relations Committee and Intelligence Committee. Kerry and Hagel are also to testify before the Senate Foreign Relations Committee Tuesday afternoon.