WASHINGTON (CNN) -- The Trump administration's deployment of additional US troops to Iraq and Syria -- and the prospect of increased operations in Yemen and elsewhere in the Middle East -- will ramp up pressure on Congress to formally authorize the war against ISIS, according to lawmakers pushing for action on Capitol Hill.

But a vote on the war threatens to expose the divisions over the US military campaign between hawks and doves that have lingered since the Obama administration began fighting ISIS in 2014.

On the one hand, congressional approval for the ISIS war could be a public affirmation of President Donald Trump's plans to accelerate the military campaign and potentially give the commander in chief a freer hand to ramp up troop deployments across the Middle East.

On the other, anti-war lawmakers could press for restrictions on troop numbers and their theater of battle, imposing limits that don't exist under the current post-9/11 authorization for fighting al Qaeda that successive administrations have until now relied on to fight ISIS as well.

The bipartisan group of lawmakers that for years has tried to force Congress to authorize the war against ISIS, arguing Congress is giving up its constitutional authority to declare war, says Trump's desire to accelerate the ISIS campaign stresses the need for a formal vote on the war.

"I haven't thought that this war against ISIS is constitutionally authorized from the beginning," said Democratic Connecticut Sen. Chris Murphy. "Now that we're talking about a potential massive increase in troop presence, we need to put some boundaries around it congressionally."

The White House has yet to weigh in directly on the issue, but like the Obama administration, the Trump administration says it has the legal authority to conduct its ISIS campaign even without congressional approval.

But one top administration official signaled the administration also sees a benefit to a new ISIS war authorization -- albeit for different reasons than many Democratic advocates.

Defense Secretary James Mattis told a Senate panel last week that he wants them to authorize the war against ISIS because, "I think it would be a statement of the American people's resolve if you did so."

"I thought the same thing for the last several years, I might add, and have not understood why the Congress has not come forward with this, at least the debate," he added.

Congress has been reluctant to debate -- let alone vote on -- a war authorization, due to an inability to find consensus as well as political concerns that a vote could be used against them later on, as Hillary Clinton's vote in favor of the Iraq War was.

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