The White House may be working hard to win the backing of hawkish Senators like John McCain and Lindsey Graham for Obama’s plan to hit Syria, but that may come at a price: It could cost the support of many Congressional Democrats who could also be key to getting Congress to grant Obama use-of-force authority.

In an interview with me today, Dem Rep. Chris Van Hollen — a key member of the Dem leadership who is also respected by Congressional liberals — was surprisingly pointed in warning that doing too much to win over the likes of McCain and Graham could end up driving him away, along with many other liberals and Dems.

“You’ve got some members of Congress, particularly Republicans in the Senate, who would like to use this resolution to open the door to large scale U.S. intervention,” Van Hollen told me. “That would be a big mistake. So to the extent that the administration tries to placate those voices, they’re going to get a lot of resistance from those of us, like me, who believe the scope needs to be significantly narrowed.”

Van Hollen declined to say whether he thought a majority of House Dems would support Obama’s request in the end. “I don’t know the answer to that,” he said. “This is a matter of conscience, and each member must make up his or her own mind. This is not an issue that will be whipped by the Democratic leadership, so the president will have to make his case to members of Congress individually.”

Van Hollen reiterated his demand for the White House’s current draft resolution to be narrowed in scope, suggesting he could not support it if his concerns aren’t met, and detailed his concerns. He said the resolution must explicitly prohibit boots on the ground; it must specify that beyond initial limited strikes, future military force can only be used in response to the use of chemical weapons; that the resolution must specify that the focus is only on deterring chemical weapon use; and that the chronological end point of the president’s authority to use force must be specified.

It is unclear whether the White House will be willing to go that far, and it is even less clear whether such tight conditions would be acceptable to the hawkish Republicans the White House is working to win over.

All of that said, Van Hollen did suggest that in general terms, the argument for the use of force was valid — a position that could frustrate those who are hoping Dem leaders will raise the bar high in demanding a good case for military action.

“The evidence is clear that the Assad forces used chemical weapons against innocent civilians,” he said. “It’s important that the international community, led by the U.S., take action, to prevent the further use of poison gas in Syria, because it would be a flagrant violation of an important 90-year-old convention and would ultimately put U.S. forces at risk of exposure to chemical weapons in future conflicts. We have national security and universal humanitarian interests at stake.”

Pressed on whether the Obama administration had really made the case that limited strikes would deter Assad in the future, and on whether the upside of strikes really outweigh the multiple risks associated with them, Van Hollen suggested the case had been made.

“I believe that through targeted strikes you could deter future use of chemical weapons by Assad,” Van Hollen said, adding: “There are risks, but there’s a larger risk in doing absolutely nothing in response to the gassing of innocent people. If no action is taken, Assad will continue to use poison gas and it will lower the barrier to use of chemical weapons in other conflicts around the world.”

And so there is the possibility of consensus among Dems, even liberals, in favor of the general idea that the U.S. should respond with force to Assad. At the same time, however, Van Hollen’s comments cast doubt on whether it’s possible to draft a use-of-force resolution — let alone define the mission itself and its general goals — in a manner that can please enough people on both sides (liberal and hawkish skeptics) to pass Congress.