Capitol Hill is growing skeptical of the U.S. military strategy in Iraq that hinges on the Shiite-led Baghdad government's ability to overcome years of sectarian divisions and strife and forge an inclusive government that shares power with Kurdish and Sunni minorities.

"Overall, I'm wondering how we can be walking down this same path that we walked down over the last decade or more and hope for a different outcome," Rep. Tulsi Gabbard, a Democrat from Hawaii, Army reservist and Iraq veteran, told top Pentagon officials Thursday.

Doubts came from both sides of the aisle when the Pentagon's two top officials appeared before the House Armed Services Committee to testify about the White House's recent $5.6 billion request to fund the ongoing fight against Islamic State extremists, also known as ISIS or ISIL.

Many lawmakers questioned President Obama's Nov. 7 decision to nearly double the number of U.S. troops authorized in Iraq to as many as 3,100. Congressional support will be essential because Pentagon officials have said additional troops will not deploy until lawmakers approve the money for the expanded mission.

Several days after Obama's authorization, about 50 U.S. troops deployed into Iraq's Anbar province for the first time in years, going to Al Asad Air Base to advise an Iraqi headquarters unit there.

The military's top officer acknowledged that the American strategy is banking on the hope that Iraqi politics will change abruptly and bring Shiites, Sunnis and Kurds together in an inclusive government.

"One of the important assumptions about this campaign is that the Iraqi government does establish its intent to create a government of national unity. I can predict for you right now, if that doesn't happen, then the Iraqi security forces will not hold together," Army Gen. Martin Dempsey, chairman of the Joint Chiefs, told lawmakers.

Some lawmakers were doubtful and noted the same sectarian conflict was at the core of the problems U.S. troops faced after the 2003 invasion of Iraq.

"Despite seven years of conflict in Iraq, 4,500 American lives lost, and more than $1.5 trillion spent, our military effort did not resolve the sectarian conflict we are now confronted with," said Rep. Niki Tsongas, D-Mass.

For now, Dempsey said he has only a "glimmer of indication" that the Baghdad government is "beginning" to move toward greater inclusion of Iraq's ethnic minorities.

Still, Dempsey and Defense Secretary Chuck Hagel told lawmakers that three months of intensive airstrikes have degraded the Islamic State, and both urged "strategic patience."

But Dempsey also said that if the Baghdad government does not follow through on its promises to be inclusive, he will recommend cutting off some U.S. military support.

"If they do not form and actually manifest this national unity agenda, then frankly ... I will be among those that recommends we do not support them to the degree that we support them," he said.

For now, it's not clear precisely what the Baghdad government can do to resolve the sectarian strife that is fueling a civil war between Sunnis and Shiites, Dempsey said.

"We don't yet know to what degree the government of Iraq will convince the Kurds and the Sunnis that it intends to have the government of national unity, one that gives the people of Iraq confidence that they have a future other than through ISIL's radical ideology," Dempsey said.

Obama has repeatedly insisted that he will not send U.S. troops back into a "combat role" in Iraq. Yet Dempsey said an Iraqi effort to retake Mosul or to restore the border with Syria may require more American boots on the ground.

"I'm not predicting at this point that I would recommend that those forces in Mosul and along the border would need to be accompanied by U.S. forces, but we're certainly considering it," Dempsey said.

He added that the U.S. has a modest force in Iraq now, and "any expansion of that, I think, would be equally modest. I just don't foresee a circumstance when it would be in our interest to take this fight on ourselves with a large military contingent."

Rep. Rich Nugent, R-Fla., urged the White House and the Pentagon to make sure they are "not glossing over the past but looking at it honestly so we can avoid making mistakes, because our men and women in uniform, their lives depend upon it."