SURUC, Turkey — There was sun and blue sky over the besieged Syrian border town of Kobani on Monday, perfect conditions for airstrikes. But for most of the day there was an eerie quiet.

From the Turkish villages nearby we didn’t hear the now familiar sounds of U.S. bombing sorties or the thuds and bangs of light artillery and tank shelling. Instead we heard the crackle of automatic gunfire and we could see gray smoke rising from the eastern side of the town. According to fighters and civilians inside, contacted by phone, this was evidence that the militants of the so-called Islamic State were torching buildings as they pulled out.

The belated uptick in well-directed and coordinated U.S. airstrikes, the stubborn almost suicidal resistance of Kobani Kurds—men and women—and Sunday night’s air-drop by U.S. military cargo planes of arms, ammunition and medical gear has shifted the balance.

Morale is lifting. Smiles light the faces of Kobani Kurdish refugees and Turkish Kurds who have watched the ebb and flow of the urban combat from this side of the border. For them, this is a battle every bit as symbolic and important as the Alamo once was to Americans. But there’s now a feeling that, unlike the Alamo, it may not end with a massacre. Like a scene out of an old Western, they’ve heard the cavalry is coming.

For days the Kurds have insisted to skeptical journalists, including myself, that Kobani would hold. They swore that the Kurdish defense forces, or YPG, although outgunned and outnumbered and armed with light weapons, would deliver the first major reversal to the Islamic State, widely known as ISIS or ISIL, since the jihadists this summer stormed across Iraq and extended their gains in Syria.

But their protestations often were marked by grim frowns or quieter caveats when they thought the formal interview over. And last week, the leader of the Democratic Union Party, or PYD, the dominant party in Syria’s Kurdistan, appeared to be preparing his supporters for defeat, saying there would be no shame in Kobani falling.

Now the men standing on the flat rooftops of one-story houses or scrambling for a better view from the top of the mosque in one village right up against the border seemed in an almost festive mood. The news had broken that the Turkish government had given the go-ahead for Iraqi Kurdish Peshmerga fighters to enter Kobani, crossing Turkish territory to reinforce the town and assist the exhausted defenders.

Activists from Turkey’s outlawed Kurdistan Workers’ Party, or PKK, the parent of the YPG, expressed their support for such a move. But they cautioned that details still needed to be agreed. Their concern is that the Iraqi Kurds, once they enter Syrian Kurdish territory, will change the political dynamic there and weaken their dominance. The key figure in Iraq’s Kurdish Regional Government, President Masoud Barzani, opposes the Syrian Kurds’ long-cherished desire to establish their own independent state.

Inside Kobani others had a different worry: that the Turks would reverse their approval of a relief force. That concession was wrung out of Ankara after immense U.S. diplomatic pressure and in the face of warnings from French and German leaders that they would start arming the Syrian Kurds, say European diplomats.

Reached by phone, Dr. Mohammad Arif, one of a handful of physicians who have stayed in Kobani in appalling circumstances, questioned whether the relief force would ever arrive.

“It is good news,” he says. “But I have no trust in the Turks. How can we trust them when they still make it difficult for us to get our wounded across the border and into Turkish hospitals? Yesterday, from nine o’clock in the morning until about four o’clock in the afternoon they held up one of our badly wounded fighters at the border, saying they didn’t have an ambulance for him.”

He accuses the Turks of making up excuses. “Let them allow the Turkish Red Crescent in here to help.” They are needed, he says, because a lot of the medical gear and medicines the U.S. dropped Sunday night was damaged.

The hard-pressed Kobani doctor isn’t the only one who will believe the Peshmerga are coming when they are manning the barricades. “Can the Turks reverse their decision?” asked a nineteen-year-old Kobani girl of her father.

Maybe that question would be better directed to U.S. National Security Advisor Susan Rice, who a week ago announced the Turks had agreed to allow American warplanes to use the NATO air base at Incirlik in southern Turkey, a few minutes flying time from Kobani, to launch airstrikes against ISIS. The next day she suffered the embarrassment of the Turks announcing that no such approval had been granted.

Kobani officials say the Peshmerga fighters are needed—or, if not them, that some other relief force must come. They don’t want to re-live the night of October 11 when the town came very close to falling and only managed to hold on because of an extraordinary last-stand resistance. The abrupt increase that night in U.S. sorties also stopped the town falling. Since then the U.S. warplanes have maintained tremendous pressure on the jihadists, coordinating their strikes with YPG commanders.

The Turkish media claim that nine American Special Forces operatives are in the town helping to direct the airstrikes. But YPG commanders deny the presence of any U.S. military personnel in the town.

Dr. Arif says the coordination is well organized and mentions the contribution in the targeting effort by an “American” who he says is fighting with the YPG, and by a Ukrainian woman. He won’t be drawn further on details about either.

These issues of whose boots are on the ground, and how many, and under whose authority, deemed hugely important inside the Washington beltway, seem like minor questions to people fighting against an enemy at the gates that crucifies and beheads its prisoners.

A colleague of Arif’s, Dr. Kurdo Abdi, gave me a first-hand account of the extraordinary demands that have been placed on the 15 doctors and nurses who remained in Kobani throughout the siege. They have struggled to provide rudimentary care for wounded fighters and civilians while dodging bombs, rockets and bullets.

“The main hospital was destroyed ten days ago by rockets,” says Abdi. The ISIS militants bombed the hospital on purpose. “Since then we have been treating people in makeshift clinics in different parts of Kobani, mainly in apartments. We have very little medicines. We got a few re-supplies from some fighters and civilians who smuggled it across the border, but very little. The situation is very bad.”

Abdi is speaking with me in front of the hospital in the border town of Suruc. He hadn’t wanted to leave Kobani but crossed into Turkey last night at the insistence of his medical colleagues. The 54-year-old trauma doctor and father of three is suffering from heart disease.

He looks gray and the dirty brown jacket he is wearing appears over-sized on him. “We do what we can,” he says. “We try to get the worst injured over here to Turkey.” I asked him whether they had the use of anesthetic. He shakes his head. “Only local,” he responds, breaking into English.

“There are thousands of civilians still inside Kobani,” he adds, and many are deeply traumatized from the month-long fighting and bombardments, but there is nothing the doctors and nurses can do for that.

The Syrian Observatory for Human Rights, a U.K.-based monitoring group that relies on activists on the ground for its information, says 374 jihadists have been killed in the month-long siege, which is more than the 258 Kurdish fighters, 20 civilians and nine Arab Syrians. Dr. Abdi says the figures probably are a bit low.

“I wanted to work there,” said Abdi. “I felt it was better to die there, then here.” He said he plans to return in three days, God willing. I asked him what sticks in his mind the most from the last four weeks. “A woman fighter who was wounded in the arm, stomach and leg and said she was fine,” he told me, “and that there was nothing wrong with her and that she should get back to fighting.”

That spirit will be needed in the days to come. Despite widespread media reports that the Islamic militants have left the town and are now just on the outskirts, that is not accurate. Both doctors say the jihadists have been pushed back on the West of the town but they are still inside parts of the center and that there is street fighting in the east and south.

And as if to emphasize their accounts, in early afternoon a U.S. airstrike hit a building in the middle of Kobani. By nightfall the relative quiet of the day was shattered by heavy clashes in the eastern part of the town along with volleys of mortars and rockets.