In his major address explaining America’s new war against ISIS, President Obama pledged that there would be no U.S. combat troops. On Tuesday, Gen. Martin Dempsey, the chairman of the Joint Chiefs of Staff, said he may recommend ground forces in the future.

The White House is seeking to gloss over the rift between the president and his top general, but it is clear that just below the waterline Obama is not on the same page as the commanders who will be leading the new fight. U.S. military officials and members of Congress have complained privately for weeks that Obama appears unwilling to commit the resources necessary to achieve his aim of defeating ISIS.

The Washington Post reported this week that Gen. Lloyd Austin, the general in charge of the military command that includes Iraq, Syria, and Afghanistan, recommended a war strategy with a small contingent of special operations forces fighting alongside Iraqi and Kurdish security forces. But Obama rejected that advice. Obama traveled to Tampa Wednesday to meet with Austin about the ISIS strategy on his own turf.

Then there was the Dempsey episode. After Dempsey acknowledged that he may recommend some ground forces in the future, the Pentagon issued a rare correction. In an email forwarded to reporters from the National Security Council as well as the Pentagon’s press office, a spokesman said Dempsey “believes the current strategy to counter ISIL is appropriate,” using the administration’s preferred acronym for ISIS. The statement added, “The context of this discussion was focused on how our forces best and most appropriately advise the Iraqis and was not a broader discussion of employing US ground combat units in Iraq.”

The internal dissent is likely to intensify with Obama’s choice of John Allen to lead the international campaign to persuade U.S. allies to pony up troops, money, and arms for his new war. Allen, a retired general beloved by Washington’s neoconservatives, has called for a robust U.S. war against ISIS since June. Obama and Allen sat down together Tuesday at the White House.

Soon after he retired in 2013, Allen took a veiled shot at his old and now new boss, observing that in the wake of Obama’s withdrawal from Iraq, “the body count is going up, the bloodletting is going up.”

As the details of the president’s new war plan leak out this week, many of Allen’s former colleagues and lawmakers wonder whether the president’s new special envoy will be able to convince Arab and European states to get behind a strategy they see as amounting to a half-measure.

Obama “has said ‘degrade and destroy,’ which makes it seem like he is more on the same page as Gen. Allen,” said Sen. John Cornyn, the ranking Republican on the Senate Foreign Relations Committee. “But I wish he would listen more to his generals and less to his political advisers, because he seems to be trying to figure out how to triangulate. You can’t triangulate this. You have to destroy ISIS by all means necessary, and I hope the president comes around to that point of view.”Sen. Bill Nelson, a Democrat on the Senate Armed Services Committee who has offered a resolution to authorize airstrikes in Syria, said Obama and Allen have the same goal even if Obama is prioritizing attacking ISIS in Iraq before attacking the group in Syria. But when asked if Obama’s Syria strategy would be enough to destroy ISIS, Nelson said, “We’ll find out.”Allen came out for destroying ISIS long before Obama. On June 12, following the president’s decision to send some military advisers to Iraq after ISIS took over the country’s second-largest city, Allen praised Obama’s decision to engage the ISIS threat in Iraq to Defense One, but he also said, “I vote for sooner and we must strike them with a hard blow.” At the time, Obama ruled out airstrikes and instead sent military advisers to assess the state of Iraq’s military.In an August 20 op-ed for the same publication, Allen wrote that ISIS “must be destroyed and we must move quickly to pressure its entire ‘nervous system,’ break it up, and destroy its pieces.”Ray Kimball, an Army strategist who worked on Allen’s staff in Afghanistan and stressed he was speaking only for himself, said, “You could certainly read his op-ed as being more expansive than what the president has authorized, but the fact that he has signed on to do this job I think speaks to what he believes can be done within the parameters of the current policy.”But others who have worked with Allen said they thought Obama’s vision for the war did not meet the objectives Allen laid out in his op-ed.Gen. Jack Keane, a retired four-star general who worked closely on the Iraq surge in the last administration, when Allen was in charge of western Iraq, said he was concerned about Obama’s pledge not to send any combat troops.“If you are serious about the ground counteroffensive, an attack up the Tigris River valley and also a counteroffensive to the west in the Euphrates River valley, if we are serious about that being successful, then you have to put the elements in there to help the ground forces to succeed,” Keane said.The general said he was also concerned that there have been no clear plans to date for the United States to reengage some of the Sunni tribal leaders who once fought against the predecessor organization to ISIS when it was al Qaeda’s franchise in Iraq.Allen worked closely with those tribal leaders during the counterinsurgency in Iraq in 2007 and 2008. But today his role would be largely limited to working with other nation-states in the coalition, according to administration officials.Keane also said found it worrisome that he did not know whether the U.S. military had contingency plans to send a more robust force into ISIS-controlled cities if initial missions led by Iraqi and Kurdish forces failed.“What happens if the ground offensive is stalled and they are not able to retake Fallujah or Tikrit?” Keane asked. “What are the contingency plans to regain the initiative? We would never go into something like this without such a plan. This would normally be U.S. and coalition brigades retaking the initiatives if the Iraqis failed.”Kimberly Kagan, the president of the Institute for the Study of War and a former adviser to Allen when he commanded coalition forces in Afghanistan in 2011 and 2012, also called the scope of Obama’s plan into question. “The administration’s strategy to me seems to be putting the United States on a path to disrupt or degrade ISIS, not to defeat or destroy it,” said Kagan, who has co-authored her own war plan against ISIS with her husband, Fred, that calls for as many as 25,000 ground forces.Several senators emerged from Tuesday’s hearing confused about Obama’s war strategy. Some Republicans saw a clear rift between the White House and the military leadership over several issues, including whether there would be a need to put boots on the ground and whether the U.S. commitment to arming the Syrian rebels was serious.“We have yet to hear a coherent strategy for victory. Having said that, people are going to support the president’s request,” Cornyn said. “If you start looking at the numbers and the difficulty we’ve had training people in Afghanistan and Iraq, it doesn’t give you a lot of confidence that that’s the solution to the problem. So we’re still waiting to hear what’s the president’s plan for victory.”At the hearing Tuesday, Defense Secretary Chuck Hagel said the Pentagon aimed to train up 5,000 Syrian opposition fighters in the next year. But the CIA’s latest estimate says ISIS has as many as 30,000 fighters under its command. Hagel acknowledged, “5,000 alone is not going to be able to turn the tide,” suggesting the war in Syria would take longer than a year.

Other lawmakers said they thought it was unrealistic to expect Syrian opposition fighters to fight only ISIS and not also turn their guns on the regime of President Bashar al-Assad.

“Why haven’t we struck a target in Syria yet? I can show the president Raqqa on the map. We can strike in Raqqa immediately,” Sen. John McCain told The Daily Beast. “We’re going to recruit people to go and fight people in Syria, but we’re not going to protect them against Bashar Assad’s airpower? That doesn’t make any sense.”