Washington (CNN) -- Some don't like war, any war. Others don't think the United States should get involved in this particular war. And some simply don't like anything President Barack Obama proposes.
Those dynamics amount to a tough challenge for Obama to win support from Congress, particularly the Republican-led House of Representatives, for his proposed attack on Syria in response to what he calls the regime's use of chemical weapons on its own people.
Obama turned to Congress after Britain's Parliament rejected taking part in any military attack on Syria, depriving the president of a normally reliable ally.
With U.N. action undermined by opposition from permanent Security Council member Russia, Obama decided to seek political cover from Congress even though he insists he has the power to act without its authorization.
Opposition comes from across the political spectrum, with liberal Democrats and libertarian tea party Republicans in rare unity against what they call an unnecessary U.S. foreign intervention.
Closer to the center, more moderate legislators from both parties say they need more answers to questions about what the mission would be and why what is happening in Syria threatens U.S. national security.
Republican Rep. Jim Risch, an Idaho conservative, summed up questions by legislators asked to decide the matter.
"The reluctance is a whole list of things, not the least of which is once you open this can, what's going to come out?" he said, adding: "I still keep hearing that the objective is, 'well we have to do something.' That's not good enough for me at this point."
Obama got a huge boost on Tuesday when the top two Republicans in the House -- Speaker John Boehner of Ohio and Majority Leader Eric Cantor of Virginia -- fully backed him.
"This is something that the United States as a country needs to do," Boehner told reporters, adding he would support the resolution authorizing military strikes on Syria and that his House colleagues "should support this call for action."
Cantor issued a statement that said America "has a compelling national security interest to prevent and respond to the use of weapons of mass destruction, especially by a terrorist state such as Syria, and to prevent further instability in a region of vital interest to the United States."
"Understanding that there are differing opinions on both sides of the aisle, it is up to President Obama to make the case to Congress and to the American people that this is the right course of action, and I hope he is successful in that endeavor," Cantor's statement said.
Despite the backing from Boehner and Cantor, it remained unclear if Obama can muster enough House Republicans to join an equally uncertain number of House Democrats to back authorization of military strikes.
In a sign of the split among Republicans, the No. 3 GOP leader in the House -- Rep. Kevin McCarthy of California -- signaled unease with supporting a resolution authorizing military action against Syria.
"Absent a clear sense of what we must do, and what the mission is, it is difficult to formulate an appropriate and effective resolution authorizing the president to use military force," said a statement by McCarthy's spokesman, Mike Long.
Tea party conservatives, who comprise a sizable minority of the House GOP caucus, have defied Boehner repeatedly in recent years. On the Democratic side, the liberal-progressive wing generally votes anti-war.
"The strike is not going to accomplish anything useful." argued Democratic Rep. Alan Grayson of Florida on CNN, adding: "We are not the world's policemen. We're not the world's judge, jury, or executioner. This is not our responsibility."
House Democratic leader Nancy Pelosi of California conceded to reporters on Tuesday that "more work needs to be done."
"In my district, I don't think people are convinced that military action is necessary, but it's important for them to know that the weapons of mass destruction use has taken us to a different place," Pelosi said after meeting with Obama.
In a letter to Democratic members on Tuesday, Pelosi urged them to share with their constituents the details of what U.S. officials say was a major chemical weapons attack by Syrian President Bashar al-Assad's regime on Damascus suburbs.
While supporting Obama's call for action, Pelosi's letter also promised her caucus a voice in the debate, saying that "the shape and content of the final resolution will depend on what members can support."
In the Senate, Majority Leader Harry Reid of Nevada is confident the Obama resolution will pass, even if it requires 60 votes to overcome any filibuster, said a Democratic source familiar with Reid's thinking.
Democratic Sen. Robert Menendez of New Jersey, who chairs the Foreign Relations panel, said in opening remarks at a hearing on Tuesday that he supported military strikes on Syria.
"This is not a declaration of war, but a declaration of our values to the world," Menendez said.
To Darrell West, the vice president and director of governance studies at the Brookings Institution, support from the House is the biggest challenge for Obama.
"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."
"We're only going to be able to help the president as much as he's willing to help himself," the aide said on condition of not being identified, noting Obama must be personally involved, make the case for military action and "prove that we have a military plan that will work and not drag us into the mud for a long time."
Meanwhile, a Democratic congressman also speaking on condition of not being identified said a "hardcore/progressive" group of Democrats will oppose the resolution, meaning the lobby effort should target "right of center Democrats who focus on national security issues and centrist Democrats."
"It is way too early to predict how the vote is going to go," the Democratic congressman said.
CNN's Deirdre Walsh, Mark Preston and Dana Bash contributed to this report.