President Barack Obama sees an end in sight to America’s “War on Terror.”

But what about terror’s war on America?

After 9/11, President George W. Bush and top officials in his administration often called the long-term, wide-ranging U.S. mission against the forces of Islamic radical terrorism the “War on Terror.”

However, Obama administration officials, including the president, have rarely used that term. And during a major defense-policy speech last Thursday at the National Defense University at Fort McNair in Washington, our current commander in chief said:

“Beyond Afghanistan, we must define our effort not as a boundless global war on terror, but rather as a series of persistent targeted efforts to dismantle specific networks of violent extremists that threaten America.”

The president said he would “engage Congress ... to determine how we can continue to fight terrorism without keeping America on a perpetual wartime footing.”

So should we call it quits from the War on Terror?

Senate Majority Whip Dick Durbin, D-Ill., and Sen. Lindsey Graham, R-S.C., gave conflicting — and revealing — answers to that basic question on “Fox News Sunday.”

Host Chris Wallace pointed out that the Cold War lasted for 40 years, then asked Sen. Durbin: “Isn’t there a danger of declaring an end to this war too soon?”

Sen. Durbin, after decrying “the McCarthy era” and “witch hunts” of the Cold War, warned that “a war-like atmosphere” can compromise “basic freedoms and liberties.” He added: “That’s what the president reminded us.”

Mr. Wallace then asked Sen. Graham: “What is your biggest practical worry about the president saying that we are in a new phase and in some sense laying out an exit strategy for the global war on terror?”

Sen. Graham’s on-the-mark response: “At a time we need resolve the most, we are sounding retreat.” He cited “emboldened” enemies, including al-Qaida forces in Iraq and Libya, and the ongoing slaughter in Syria.

Sen. Graham rightly asserted: “The challenge of our time is to keep weapons of mass destruction out of the hands of radical Islamists, and we are failing in my view. ... Iran is marching toward a nuclear weapon. And we show this lack of resolve, talking about that war being over. What do you think Iranians are thinking?”

And: “I’ve never been more worried about our national security than I am right now. And the speech did not help.”

The president’s speech did at least clarify — well, sort of — his future use of drones against terror targets. He still plans to order such strikes when he deems them necessary, but in a more limited manner, with codified “guidelines, oversight and accountability.”

The president also restated his so-far-unfulfilled commitment to closing the U.S. prison for terror suspects at Guantanamo Bay, Cuba. As part of that push, the president last week lifted the ban on transferring Gitmo detainees to Yemen, the native land of a majority of those prisoners.

Yet as The Associated Press reported: “Obama’s decision is not without risk — detainees who have been released to Yemen in the past have joined terrorist fighters in the Arab nation.”

Fortunately, fears that the Obama administration will propose using the U.S. Consolidated Brig Charleston in Hanahan as a site for trying Gitmo prisoners in the U.S. appear far-fetched — as of now.

After all, conducting such trials near any U.S. population center would create a serious new menace to large numbers of American civilians.

But terrorism’s threat to Americans endures — here in the United States and around the world.

And again, ending our “boundless global war on terror” won’t end terror’s boundless global war on us.