Two former U.S. officials told POLITICO that Lindsey Graham (R-S.C.) has been urging the White House directly to leave a small presence, made up of U.S. special operations forces and potentially CIA paramilitary officers, on the ground to maintain pressure on the Taliban and continue counterterrorism operations against al Qaeda and the Islamic State.

Those ideas would seem to cut against the terms of the agreement signed on Saturday, under which the United States agreed to withdraw all of its forces within 14 months. In exchange, the Taliban agreed not to allow al Qaeda or other groups and individuals “to use the soil of Afghanistan to threaten the security of the United States and its allies.”

Leaving a residual force in Afghanistan is in line with Trump’s previous comments, however. Last year, he hinted that he would keep forces on the ground, including “high intelligence,” to allow the United States to react quickly to any attack on U.S. interests.

But terrorism analysts are skeptical that the Taliban intends to follow through on its end of the bargain, and Graham likewise urged caution during a Monday appearance on Fox News.

“We have a chance to end this war in Afghanistan smartly and well,” said Graham, who is known to have Trump’s ear on foreign policy issues. “But we’re going to need a residual U.S. force, a counterterrorism presence for years to come, because I don’t trust the Taliban to police al Qaeda and ISIS.”

After reports emerged that the Taliban had resumed attacks on Afghan forces, Graham tweeted his concerns. “Always suspicious of the Taliban when it came to any peace agreement, but can’t believe they’re this stupid,” Graham tweeted Tuesday. “Killing 5 Afghan police officers not only violates the spirit of the alleged peace deal, it violates the letter of the agreement.”

Asked for comment on Graham’s private outreach, a Graham spokesperson, Kevin Bishop, said: “He’s been calling for a residual force in Afghanistan since the Bush administration.” A National Security Council spokesperson did not respond to a request for comment.

This is not the first time Graham has tried to sway the president on a key foreign policy issue. In the days after Turkey invaded northeastern Syria, Graham was apoplectic, and said the U.S. decision to abandon Kurdish allies in the area was a “stain on America’s honor.” Along with retired Army Gen. Jack Keane, another occasional informal Trump adviser, Graham walked the president through a map of Syria, Turkey and Iraq, pointing out that northern Syria’s rich oil fields would fall into Iran’s hands if Trump withdrew all U.S. troops from the country. Trump ultimately backtracked, leaving roughly 800 U.S. troops there — officially, to guard the oil fields.

Retired Army Gen. Jack Keane. | Alex Brandon/AP Photo

In recent days, Keane has also appeared on Fox News and spoke to POLITICO about his concerns regarding the Afghan peace deal, which calls for U.S. forces to begin withdrawing immediately from Afghanistan. Under the terms of the agreement, some 5,000 troops will leave within 135 days.

“What we are being told by people in the Pentagon is that this is a conditions-based withdrawal, but the agreement does not identify those conditions,” he told POLITICO, also noting concerns about protection for civil liberties and human rights. “It’s all aspirational.”

One Republican member of Congress who’s also a military veteran said he had “significant misgivings” about the agreement. “This seems like a pretty crummy deal,” he said. “If this were an Obama deal, we would be crushing him for it. It feels like a retreat. It feels like a concession.”

But the member, who asked not to be named, acknowledged that his voters are with Trump — he estimated that roughly only 20 percent of his district supports staying.

In the House, Rep. Liz Cheney (R-Wyo.) has led the opposition to the deal, but she was only able to round up around two dozen fellow members last week to sign a letter to Secretary of State Mike Pompeo and Defense Secretary Mark Esper expressing “serious concerns” about the agreement.

“President Trump has taken crucial action to keep our nation safe, including eliminating the world’s most dangerous terrorists and destroying the ISIS caliphate. He knows a bad deal when he sees one,” the lawmakers wrote.

Other Republican members are tentatively supporting the deal, but are openly skeptical it will actually work. Rep. Don Bacon (R-Neb.), a veteran of Afghanistan, said he would like to bring up his concerns about the deal with Trump the next time he sees him.

“I’m only nervous about it because the Taliban have never been an honest negotiator when you come to the table with them and as far as I can tell they’ve always been allied with al Qaeda even though they’re showing here that they’re not in the agreement,” he said. “I’m going to support it but mainly because it has a window of time that we can put the breaks on it, but I’m not ringing the bells or blowing the trumpets on this thing because I do not trust these guys.”

Former and current officials said discussions last year centered on leaving a residual force in Bagram and the embassy compound consisting of special operations forces and intelligence assets to carry out targeted strikes and maintain awareness of terrorist activity in the country. One course of action called for the CIA to take over more of the mission as conventional troops pulled out. However, that proposal has been largely discarded after the CIA pushed back.

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Keane also expressed skepticism with the proposed prisoner exchange, an issue that has already threatened to derail the deal. On Monday, the Taliban refused to take part in intra-Afghan talks, one of the conditions of a full withdrawal of U.S. troops, until the Afghan government releases roughly 5,000 Taliban prisoners.

“Prisoners are normally exchanged after there has been a bonafide peace settlement,” Keane said.

Republican hawks have been far less polite in private, lambasting the deal in scathing terms.

"Frankly, if this was negotiated by Barack Obama, the Republican base would go apeshit,” one senior Republican national security aide said.

One former Trump administration official acknowledged the widespread skepticism within Republican ranks, but noted that the timing of the pullout allows the president to tout it on the campaign trail as a promise kept.

“Then it’s a second-term problem,” this person said. “He can say the Taliban — they’re full of crap.”

Meridith McGraw contributed to this report.