"There are very few moderates that are left and it's a highly polarized institution," he noted, adding that what amounts to a war authorization vote was likely to shake up the normal partisan line in Congress.
"You could have libertarian Republicans joining liberal Democrats to vote no, just because they're tired of foreign adventures," West said. "It may come down to Republicans who support a strong foreign policy joining forces with Democratic moderates to give approval."
A new ABC News/Washington Post poll released Tuesday showed that nearly six in 10 Americans oppose military strikes against Syria, with similar results from respondents identifying themselves as Democrats and Republicans.
The administration has launched what it calls a "flood the zone" lobbying effort to persuade legislators to support the resolution authorizing military strikes against Syria.
This effort in Washington includes classified briefings, testimony of Cabinet members at committee hearings, and meetings with the president.
Mindful of concerns that a strike on Syria will lead to a prolonged engagement, Obama said Tuesday that "this is not Iraq, and this is not Afghanistan."
"This is a limited, proportional step that will send a clear message -- not only to the Assad regime, but also to other countries that may be interested in testing some of these international norms -- that there are consequences," the president said.
At the hearing by the Senate panel he used to chair, Secretary of State John Kerry later said that "neither our country nor our conscience can afford the cost of silence."
However, Obama departs on Tuesday night on a four-day trip to Sweden and Russia at a time when members of both parties clamor for him to be directly involved.
With congressional elections next year, many legislators feel that the safe vote on Syria right now is to oppose the Obama resolution, CNN Chief National Correspondent John King said Tuesday.
"The president has to sway and the most important people he'll meet with today are the House Republicans," King said. "He doesn't have good relationships with them, very few personal relationships with them. They don't trust him. They don't support most of his other policy initiatives."
Speaking before Boehner and Cantor publicly backed Obama, King said the president needed the House GOP leadership to "lobby their own members, saying this is the right thing to do even if you don't agree with the president."
Cantor's statement did just that, even taking on a popular GOP talking point that Obama had erred by previously declaring chemical weapons use a "red line" that would bring a U.S. response if Syrian President Bashar al-Assad crossed it.
"The United States' broader policy goal, as articulated by the president, is that Assad should go, and President Obama's red line is consistent with that goal and with the goal of deterring the use of weapons of mass destruction," Cantor said in the statement. "It is the type of red line virtually any American president would draw."
However, Boehner's spokesman, Michael Steel, made clear that the speaker was leaving it to Obama to persuade legislators to support him.
"It is the president's responsibility to make his case to the American people and their elected representatives," Steel said in a statement, adding that "all votes authorizing the use of military force are conscience votes for members, and passage will require direct, continuous engagement from the White House."
Obama met Monday with two veteran Republican senators -- John McCain of Arizona and Lindsey Graham of South Carolina -- who emerged to say they could support a more precise and robust strategy than the president initially outlined.
In particular, McCain and Graham said Obama pledged increased military aid to opposition forces in Syria that would bolster their fight against al-Assad at the same time as U.S. military attacks expected to to involve cruise missile strikes on Syrian military command targets.
After Obama met Tuesday with Boehner, Pelosi and the chairs of several national security committees in Congress, legislators from both parties said they expected the initial resolution proposed by the president to be revised to address their concerns.
In particular, they said it would define the mission more narrowly and specify no "boots on the ground," which means no U.S. troops would be deployed to Syria.
West noted that no matter what lobbying takes place, "there are some Republicans who will vote 'no' just because the idea came from President Obama" because "they detest everything he stands for."
Moderates, meanwhile, may face the prospect of a primary challenge from the more extremist wing of their respective party if they authorize a war resolution, he said.
"Anti-war sentiment remains very strong within the Democratic Party," West said, noting that grass-roots activists on the left opposed the Iraq war at the height of post 9/11 patriotic fervor. "The idea of another foreign intervention would be of great concern to those people."
In the end, West said he expects Obama's resolution to win approval because "the president has laid national prestige on the line."
However, a House GOP leadership aide told CNN that "it is going to be a big lift to get this done."