Washington (CNN) Congress is considering placing new limits on the Trump administration's war-making powers as the White House delegates key decisions on military action to the Pentagon.

Democrats and some key Republicans say they're alarmed that President Donald Trump has delegated the decision to set troop levels in Afghanistan to his defense secretary, James Mattis, particularly when the administration has yet to outline its larger strategy for the longest war in US history.

And the US military's shooting down of a Syrian government jet on Sunday has injected new urgency for advocates in Congress who want to pass an authorization for use of military force against ISIS -- which could at the same time limit military action against Syrian President Bashar al-Assad's regime.

Lawmakers say that the escalating military action in Syria -- including the jet shootdown, commanders' increased authority to take military action and Trump's decision in April to launch missile strikes against government targets -- underscores the need for Congress to reassert its constitutional authority to authorize war.

"With this President quietly delegating authorities to the secretary of defense and commanders of the field, I think it's critical that this committee and the Congress as a whole embrace our oversight duties," said Sen. Robert Menendez, a New Jersey Democrat who was Foreign Relations chairman when the committee voted on an ISIS war authorization in 2014.

"We've had nine Americans killed in combat missions this year. Campaigns have ramped up, I read about a surge in Afghanistan. And I continually don't have a sense of what the totality of the strategy is," Menendez added.

Still, Congress faces major hurdles to passing legislation that could authorize the use of force against ISIS or the Assad regime, as the balance of war-making power has markedly shifted toward the Executive Branch under both the Obama and Trump administrations. In addition to deep divisions about whether Congress should limit the commander in chief over where and when he can deploy troops in the war on terror, many in Congress are wary about taking a politically difficult vote on the ISIS war.

A 16-year-old war authorization

The Obama and Trump administrations have relied on the war authorization that passed right after the September 11, 2001, terrorist attacks as legal justification for military action against ISIS. Joint Chiefs of Staff Chairman Gen. Joe Dunford said that authority also provided the justification for the US to shoot down a Syrian jet that was threatening US-backed forces.

The recent military action against the Assad regime -- the US military also shot down a pro-regime drone on Monday -- has amplified concerns that the war authorization is being stretched too far, and Congress needs to step in.

"You can't justify going after ISIS under the 2001 (Authorization for Use of Military Force, or AUMF), let alone going after Syrian aircraft," said Maryland Sen. Ben Cardin, the top Democrat on the Senate Foreign Relations Committee. "That is absolutely absurd."

The foreign relations committee held a hearing on a war authorization Tuesday that's authored by Sens. Tim Kaine, a Virginia Democrat, and Jeff Flake, an Arizona Republican. Their bill would sunset the 2001 war authorization and provide new authority to go after ISIS, al-Qaeda and other associated terrorist groups but it would not include authority for attacking the Assad regime.

Tennessee Sen. Bob Corker, the committee's chairman, expressed a desire to pass a new war authorization but he also expressed some skepticism that Congress would be able to do so.

"Some members of Congress will use this debate for the singular purpose of imposing limitations on our president. It's just a fact," Corker said. "Others may refuse to limit a president at war in any way. That's a fact. And that's a wide gap to bridge."

Afghanistan troop decisions

The White House last week gave the authority to set troop levels in Afghanistan to Mattis amid an internal disagreement among administration factions over the best path forward there.

The Pentagon is considering an increase of 3,000-to-5,000 troops in Afghanistan to help bolster the Afghan forces in their fight against the Taliban.

Trump himself has said very little about the 16-year-old war since becoming president, as well as during the 2016 presidential campaign.

And the move has sparked criticism from Democrats that Trump is disinterested in fulfilling his duties as commander in chief, as well as concerns about the over-militarization of his administration. While Mattis is the civilian leader of the Pentagon, he's also former Marine general, and Trump's national security adviser H.R. McMaster is an active-duty three-star Army general.

"I think it's an abdication of a core executive responsibility, setting troop levels," said Sen. Chris Murphy, a Connecticut Democrat. "Viewing Afghanistan only through a military lens will continue us down a rabbit hole of failure. The fact the President is supposed to be looking at every component of the Afghanistan strategy, and he's basically outsourced the Afghanistan issue to the military, which clouds the fact that Afghanistan is more so a governance problem than it is a military problem."

To many Republicans, however, Trump's decision is a sign he's listening to commanders in the field, and is a response to criticism of the Obama White House that it was micro-managing military action and setting artificial withdrawal dates for Iraq and Afghanistan.

"That's essentially what he said he's going to be doing — he's going to rely on the uniforms as opposed to what we've been looking at the last eight years," said Oklahoma Republican Sen. Jim Inhofe.

But the Trump administration still has not laid out its strategy for Afghanistan either, which has drawn the ire of a key Senate Republican, John McCain.

McCain ripped into the White House and the Pentagon on Tuesday, issuing a warning that he was prepared to give the Trump administration an Afghan strategy if it would not set one for itself.

"The President has two choices: either give us a strategy or we will put a strategy that we develop into the defense authorization bill," McCain said. "We're talking about shooting down airplanes in Syria. We're talking about Afghanistan, that there's going to be X-thousand troop increase. And yet no one has informed the American people and this committee. So I have to say that I want some answers."