Washington (CNN) - New York Republican Rep. Peter King, a supporter of military action in Syria, and several other House GOP members met with White House Chief of Staff Denis McDonough Monday at the White House to discuss Syria and the president's speech Tuesday night.
King declined to identify the whole group, but said Reps. Tom Cotton, Mike Pompeo, and Intelligence Committee Chairman Mike Rogers – all of whom back the president's plan in Syria – were among those in the meeting.
"The overriding thing was that the president has to make it clear that this a national security issue," King told CNN.
"This is not Obama's war – this is a military strike that is in our national interests," he added. "He [the President] needs to make that clear – how central it is."
King said that Secretary of State John Kerry's statement earlier Monday describing potential U.S. military action as an "unbelievable small" attack doesn't help convince people.
"The other thing is that they have to show that they are serious about it," King said.
Referencing the president's televised address scheduled for Tuesday night, King said it's important that he explains the case more clearly, telling CNN so far "there's basically not been a totally coherent policy."
The New York Republican said "there is large scale opposition," and among the group of those on the Hill supporting the president "none of us are winning votes for being there."
King said the issue of the latest Russian proposal for Syria to hand over its chemical weapons did come up in the meeting, but he did not want to characterize how McDonough responded to it.
King was skeptical of Russia's proposal, saying "I have a hard time trusting the Russians. I don't want to prejudge it right now. We want to make sure it's not a delaying tactic. I have a hard time seeing Assad giving up his chemical weapons."
King praised McDonough as a "straight shooter" and said he was a "good messenger" to talk more broadly with House Republicans. He said now that members are back in town from the August recess, the White House should take advantage and ramp up efforts to meet with GOP members.
On his way into the meeting, King ran into former Secretary of State Hillary Clinton, who was reviewing her prepared remarks on Syria with her aides.