The big news in my hometown of Worcester, Massachusetts. this month has been the appearance, near a major highway, of a billboard criticizing America’s foreign aid to Israel. “We give Israel $10 million a day! That money could send our kids to college,” the sign reads.

It’s the most recent offensive in a nationwide campaign. Similar signs have cropped up in Orlando, Fla.; in Northern California, in Des Moines, Iowa, and in at least a dozen other cities, according to the Anti-Defamation League.

A reality check is in order. The roughly $3.1 billion a year in foreign military financing grant aid that America does give to Israel actually does help send American youth to college. About three quarters of the money is spent to purchase American military supplies. Plenty of machinists at Lockheed Martin, engineers at Raytheon, and employees at plenty of other American defense contractors have sent their children to college based partly on work filling purchase orders for the Israeli military.

Second, those funds are a rounding error compared to what American taxpayers already spend on federal, state, and local government aid to higher education. In 2013, that was $157.5 billion, plus at least another $50 billion or so in subsidized loans and tax credits and deductions. Richard Vedder’s research shows colleges tend to increase tuition by the amount that the government increases financial aid. That means channeling Israel’s military aid to American colleges instead might further increase pay for professors and administrators at American colleges, but wouldn’t much help most tuition-paying parents or students.

The billboard is a classic false dichotomy, creating an imaginary binary choice between aiding Israel and aiding American college students. It leaves out the possibility that the military aid is a win-win, and that Israel’s presence on the front lines against radical militant Islamist extremism actually makes it less likely that those American students will be attacked or drafted into war.

There’s longstanding broad and bipartisan congressional support for military aid to Israel. But increasingly, the gist of the billboard’s message — that American involvement or aid overseas comes with an unacceptably high price at home — is heard in the mainstream of American politics.

Donald Trump’s presidential announcement speech featured this line: “It is necessary that we invest in our infrastructure, stop sending foreign aid to countries that hate us and use that money to rebuild our tunnels, roads, bridges and schools.” He wasn’t talking about cutting aid to Israel specifically, but the overall message is to bring home funds that were once spent abroad.

Nor is Mr. Trump an outlier. Senator Rand Paul, a Republican from Kentucky, said in announcing his own presidential candidacy, “Let’s quit building bridges in foreign countries and use that money to build some bridges here at home.”

These Republicans are echoing Barack Obama. Campaigning for the presidency in 2008, he said, “When we spend $10 billion a month in Iraq, that means less money to fix crumbling roads and bridges here at home.” If you’ve driven over a pothole lately, you can testify to the reality that seven years of the Obama presidency and the official end of the Iraq War have somehow, nonetheless, not conspired to render our roads anywhere near flawless.

In another campaign speech, Mr. Obama said, “For a fraction of what we’re spending each year in Iraq, we could be giving our teachers more pay and more support, rebuilding our crumbling schools, and offering a tax credit to put a college degree within reach for anyone who wants one.”

Mr. Obama, in framing spending on Iraq as a choice against tax credits for putting college degrees “within reach,” sounds just like the author of the anti-Israel billboard in Worcester.

Sure, plenty of foreign development aid is squandered or counterproductive, as William Easterly has documented in books such as “The White Man’s Burden” and “The Tyranny of Experts.” Israel itself may not want or need American help forever. Bashing the pro-Israel lobby that presses to get the aid approved each year — and that has its annual meeting in Washington this week — has become fashionable even among American Jews, at least in certain circles.

Reasonable people can certainly come down in different places on the proper ratios of America’s foreign and domestic expenditures. But imagining that America can scale back its overseas commitments cost-free — without creating a power vacuum to be filled by our rivals or enemies, or chaos that will eventually spread here — is a fantasy. So too is the notion that any funds reallocated in such cuts will make a big difference in the overall federal budget, or in that of any ordinary American family.

Mr. Stoll is editor of FutureOfCapitalism.com.