(CBS News) It's "an uphill slog" for President Obama to get enough lawmakers on board to authorize his request for military intervention in Syria, House Intelligence Committee Chairman Mike Rogers, R-Mich., said Sunday on "Face the Nation," just days before Congress is expected to vote on the resolution.
"They really needed to start two years ago on this process and really haven't done it, so they don't have strong relationships in Congress today," Rogers said of the administration. "And, candidly, [they] have done an awful job explaining to the American people what is in our national security interests in any level of engagement in a place like Syria."
Rogers said he backs a "very limited" strike in the civil war-torn country amid mounting evidence that President Bashar Assad used chemical weapons against his own people. But Mr. Obama's campaign for such a move - including his surprise announcement during August recess to seek congressional approval, a move typically reserved for boots-on-the-ground scenarios - has been "mystifying."
"I completely understand why people are skeptical of this," Rogers said. "You have a reluctant commander-in-chief, first of all, who's trying to come to the American people and say, 'I'm going to do something but I'm not going to do a lot; I'm not sure exactly what we're trying to do.' I mean, that's what the American people are hearing. And hearing that, I'm skeptical as well."
Though feedback from his constituents has been overwhelmingly against striking Syria, Rogers said, his vote on the resolution "cannot be about Barack Obama; it has to be about what is in the best interests of the United States of America.
"...If we just make it about us," he said, "being Congress or the American people, against our frustrations against this president, we miss the big picture about what is in the best interests of U.S. national security interests. Small and effective now save big and ugly later. So we're either going to pay this price now or we're going to pay a bigger price later."
There's "no doubt about it," though, that the bulk of Americans oppose U.S. involvement in Syria, Rep. Elijah Cummings, D-Md., said later on the program; Rep. Justin Amash, R-Mich., in the same segment, agreed.
Amash said in town halls across his state he has gauged "not just disapproval of the war - overwhelming disapproval - from Republicans, from Democrats. And when you're dealing with an issue like war, you must take into consideration what the public thinks. You're asking people to possibly send their loved ones into harm's way.
"...Based on the objectives that the administration has laid out, based on the strategy they've laid out," Amash continued, "I can't come up with a reason right now why the United States should support this action."
With an eye on the House's more limited resolution than what passed the Senate Foreign Relations Committee last week, Cummings said "it's possible" he could still get behind the president's request. Mr. Obama will make his final plea with remarks to the nation Tuesday at 9 p.m.
"He's got to show, first of all, that this is in our core national security interests, and why it is," Cummings said. "He's got to show that if we don't completely degrade Assad's capability, how do we make sure we still deter him from using these chemical weapons? And then he's got to show us that this will not end up in a scenario where we are finding ourselves in deeper involvement in a civil war over there in Syria. These are difficult issues he's got."
© 2013 CBS Interactive Inc. All Rights Reserved.