U.S. forces have now surpassed 2,800 strikes against targets in Iraq and Syria under President Obama’s war against the Islamic State, all as part of a conflict Congress has yet to specifically authorize — and amid worries lawmakers won’t ever act.

Under intense pressure from Capitol Hill, Mr. Obama finally submitted a draft authorization for the use of military force against the Islamic State in February, but it’s since languished, caught in the stalemate between those who want tighter restrictions and those who want the president to have as free a hand as possible.

Now analysts worry that inaction will set a dangerous precedent and leave Congress shorn of its warmaking powers.

“I understand it’s unlikely that they’ll act, but it’s important for them to act,” Shoon Murray, an associate professor in the School of International Service at American University, said last week. “It does take away the war powers of Congress by Congress‘ own deference.”

The U.S. military has been conducting strikes in Iraq for 10 months, and began striking directly at targets in Syria last September as part of Mr. Obama’s announced campaign to degrade the capabilities of the Islamic State.

This past weekend’s attacks brought the total to 1,458 strikes in Iraq and 1,343 in Syria by U.S. forces. Coalition forces allied with the U.S. have conducted another 655 attacks on Iraqi targets and 95 in Syria.

Mr. Obama has justified the attacks under his commander in chief powers and under the 2001 resolution authorizing force against al Qaeda, and the 2002 resolution authorizing the ouster of Saddam Hussein in Iraq.

Some lawmakers on Capitol Hill have said Mr. Obama is stretching those laws and that the strikes could be illegal — though they say they want to put them on firm footing by passing a new authorization.

But first Mr. Obama balked at sending up new war language and, when he finally did, the split on Capitol Hill became clear: The draft authorization was too aggressive for some, chiefly Democrats, who wanted tighter restrictions on ground troops. But it was too narrow for hawks, chiefly Republicans, who would prefer the president to retain all options.

“Obviously, it is not going anywhere,” Sen. John McCain, Arizona Republican and chair of the Senate Armed Services Committee, told Defense One last week. “The proposal was not enough for those on the left and way too much for those of us who believe that the Constitution says the president is the commander in chief.”

Sen. Bob Corker, Tennessee Republican and chair of the Senate Committee on Foreign Relations, which would consider the authorization, told reporters last week that he is starting discussions to look for a bipartisan path forward, but will not bring it up if partisan debates on the authorization could give the impression that lawmakers are divided on fighting the Islamic State.

Political analysts said the stalemate is bad for Congress, which is granted the power to declare war under the Constitution, while the president is granted the powers of commanding the armed forces.

“You have this structure of checks and balances in place. The problem is, it’s not being followed,” said Chris Edelson, assistant professor of government at American University. “The system depends on each institution asserting its power, and that’s not happening.”

The president, in his February draft, requested authority to use military force for three years, allowing the administration to strike the Islamic State anywhere in the world, though the use of ground forces outside of limited roles like advisers or search-and-rescue is prohibited.

Complicating matters is the 2001 authorization to use force against al Qaeda, which would remain in effect. Since the president has argued the current war is legal under that authorization, which has no endpoint, even the expiration of a new authorization against the Islamic State wouldn’t necessarily halt the war.

That leaves the administration free to pursue its war without having to get new permission from Congress.

Mr. Edelson said it wasn’t long ago that Congress did flex its war powers. When Obama wanted to strike Syria to stop the Assad regime in 2013, enough lawmakers publicly demanded first Mr. Obama seek their permission that he backed off his plans, creating space for Russian President Vladimir Putin to broker a deal.

“Congress has shown it is capable of asserting itself,” Mr. Edelson said.

For Mr. Obama, his unilateral stance is also an about-face from his time as a senator, when he argued Congress needed to keep the president from acting unilaterally in declaring war, Mr. Edelson said.

“The president does not have power under the Constitution to unilaterally authorize a military attack in a situation that does not involve stopping an actual or imminent threat to the nation,” Mr. Obama said during a 2007 interview with The Boston Globe.

“As president, unfortunately he doesn’t follow that approach,” Mr. Edelson said, noting that the president has conducted unilateral strikes in 2011 in Libya before his campaign against the Islamic State.