A year ago today, the Iraqi city of Mosul fell to Islamic State militants, an event that should have shattered any lingering illusions that Islamic State was the "JV" of radical Islamic terrorist groups. For the past 12 months we have seen its vicious campaign to establish a new Caliphate carved out of Syria and Iraq play out on computer and television screens across the globe. We have seen American, Israeli, British and Japanese captives beheaded. We have seen a brave Jordanian pilot burned alive. We have seen mass executions of Egyptian Christians. We have seen the civilian populations of Syria and Iraq brutalized, with woman and children crucified, raped, tortured and forced to accept the Sharia law imposed by the Islamic State.

While these atrocities have grabbed the headlines, Islamic State has also been engaged in a steady campaign of territorial expansion, both in the region and beyond. Other major Iraqi cities, including Fallujah and Ramadi, have fallen to the Islamic State. It has extended its operations to Libya and allied with Boko Haram in Nigeria. So-called "lone wolf" plots to attack us here at home have cropped up from Texas to Massachusetts.

Just this week, the Islamic State has captured dozens of Eritrean Christians in Libya and announced its intention to conquer the Iraqi capital of Baghdad, a threat that may be more sensational than real, but which demonstrates its broadening ambitions. Even more disturbingly, reports are surfacing that the Islamic State may be working on chlorine-based chemical weapons and even a crude "dirty bomb" fashioned out of the radioactive material seized from Iraqi medical facilities.

Even so, Islamic State is not yet invincible, and we should not fall into the trap of thinking it cannot be defeated. Determined efforts against it have proved effective, for example at Tikrit in Iraq and Kobani in Syria. But Tikrit was captured by the Iran-backed Shiite militias, some of whom have proven almost as vicious as the Islamic State. Kobani was defended by the Kurdish Peshmerga forces, not the Iraqi Security Forces (ISF). And these defeats have proven isolated events, while the larger momentum has been in Islamic State's favor.

It's time to tell the American people the truth. One year into the program, we must admit that the Obama administration strategy, which has consisted of a limited U.S. air campaign, a program to train and equip the ISF and a directive to achieve sectarian political reconciliation in Baghdad, is failing.

Unfortunately, the administration cannot see this simple truth. While the president did admit this week that his strategy is imperfect and lacking in details, his solution appears to be more of the same as he recommended more trainers and made increasingly desperate pleas to Baghdad to fill in the blanks.

Enough. We can't afford another year of deliberation and half-hearted measures that will only further embolden Islamic State and tip it toward victory. What we have been doing isn't working, and doubling down on a failed strategy will not result in success. There are still choices besides continuing President Obama's botched strategy, or re-deploying tens of thousands of American combat troops to Iraq.

For starters, we have to stop understanding the mission against the Islamic State as an extension of the 2003 invasion to topple Saddam Hussein, which then mushroomed into an effort to turn Iraq into a western-style democracy. Our mission now should be to destroy the Islamic State terrorists whose avowed purpose is to harm America and our allies, not to turn Iraq into a democratic utopia.

Given the dysfunctional state of Iraq, we also need to let go of the fantasy that the ISF is going to be our boots on the ground. The fact is, as Pentagon spokesman Col. Steve Warren admitted this week, that we simply do not have the requisite number of Iraqi recruits to make this strategy effective. It doesn't matter how many trainers we send if there is no one there for them to train.

The goal of political reconciliation in Baghdad, which the administration has also prioritized, has proven equally illusory. We are marking another unhappy anniversary this month—the anniversary of Haider al-Abadi becoming prime minister of Iraq. While Shia, there were hopes among the Sunni Arab nations such as Egypt and Jordan that Mr. al-Abadi would reverse the disastrous sectarian policies of his predecessor, Nouri al-Malaki, and bring Iraq together to fight the existential threat of the Islamic State.

However well intentioned he may be, however, Mr. al-Abadi has not been able to perform this miracle. Surrounded by entrenched al-Maliki loyalists, he has taken no significant actions to reduce the militant Shiite influence of Iran or to liberate the Sunni territory invaded by Islamic State. Absent a dramatic shift in the prime minister's policies — something that would have to come from within his administration and cannot be imposed by the U.S. — making political reconciliation in Baghdad a keystone of our strategy dooms it from the get-go.

It is time to shake free of the failures of the past year and engage in some fresh thinking. In last weekend's Washington Post, retired Air Force Lt. Gen. David Deptula proposed an alternative strategy, which would consist of exploiting our asymmetric advantage over the Islamic State through an overwhelming air campaign unfettered from the rigid and restrictive targeting rules ostensibly designed to protect civilians, but which have effectively enabled Islamic State to continue oppressing them. The recent election in Turkey, a rebuke to the anti-American President Tayyip Erdogan, who has refused us access to the NATO air base at Incirlik, might present an opportunity for us to press for use of this vital asset.

We might also look into by-passing Baghdad to arm the Kurds directly to ensure the free flow of ammunition and heavy weapons, and then embed our special operations troops with them to provide the targeting intelligence our air campaign requires. The Kurds have proven their value in battle against Islamic State, and we should allow them to help us while providing them the assistance they need.

For our allies such as Israel, Jordan and Egypt, such actions would be a welcome demonstration of decisive and engaged American leadership. The United States is blessed with the greatest fighting force in the history of the planet, and the destruction of the Islamic State is not beyond our capability, especially when we work with our effective regional partners. But if we hope to get the job done before it is too late, we must make clear that that is of our mission.

Sen. Ted Cruz, R-Texas, is seeking the 2016 Republican nomination for president. Thinking of submitting an op-ed to the Washington Examiner? Be sure to read our guidelines on submissions.