While congressional pressure has increased for the U.S. military to intervene in the violent civil conflict in Syria, not everyone on Capitol Hill is calling for immediate action.

The Senate’s No. 2 Republican, Minority Whip John Cornyn of Texas, on Tuesday said President Obama must make the case to the American people and consult with Congress before launching a strike against Syria.

The president “needs to explain what vital national interests are at stake and should put forth a detailed plan with clear objectives and an estimated cost for achieving those objectives,” he said in a prepared statement.

Sen. Tim Kaine, D-Va., said that while the Syrian government’s reported use of chemical weapons on its own people is despicable, “absent an imminent threat to United States national security, the U.S. should not be engaged in military action without congressional approval.”

“While it’s important that we continue to work closely with our allies to help Syria achieve a negotiated, inclusive political solution, those who employ such weapons and indiscriminate violence must be held accountable,” he said.

Sen. Bob Corker of Tennessee, the senior Republican on the Senate Foreign Relations Committee, also called on the president to coordinate with Congress on any attack aimed at Syria, though he said “the appropriate person” briefed him Monday of the situation.

“I think the White House has confirmed they believe that to be a consultation,” the senator told MSNBC’s “The Daily Rundown” on Tuesday.

Corker said a U.S.-led attack on the Middle East country appears inevitable — a move he says is “the right thing to do as long as it’s surgical and proportional.”

“What I don’t want to see is … is something that ends up causing us to be mired in the civil war,” he said.

But with evidence mounting that Syrian President Bashar al-Assad’s government used chemical weapons, Sen. Bill Nelson, D-Fla., said the United States must act now.

“There should be moral outrage over the use of chemical weapons on innocent civilians in Syria,” said Nelson, a member of the Senate Armed Services Committee. “At this point I believe it appropriate to take military action with NATO and our regional allies.

“Inaction would only lead to greater suffering and instability in the region and would further embolden Assad.”