There are many solid arguments for why the United States should not grant legal status to illegal immigrants, as proposed in the Senate immigration reform bill quashed last month.

But throughout the immigration debate, one particular mantra was heard from opponents of legalization, perhaps more than any other: “My ancestors came here legally.”

So too, the argument holds, must today’s immigrants. We’re a nation of laws, we must be consistent, and we must not reward lawbreakers. It’s a mighty handy argument that worked wonders for opponents of the legalization bill. It’s logical and draws a clear moral distinction between previous generations of law-abiding immigrants and today’s border-jumpers. It heads off allegations of xenophobia, allowing the speaker to say it’s not immigrants he or she is against, just illegality.

It works, too, because it rings true with Americans. The images burned into our brains of previous immigration waves come largely from newsreels and photos of immigrants disembarking at Ellis Island, one at a time, orderly, legally.

There’s one problem with the argument. It’s utter hogwash.

First of all, for hundreds of years, as immigrants poured in by the hundreds of thousands from the 1600s to the early 1900s, there were simply no federal immigration laws to break. Unless you were a criminal or insane (or after 1882, Chinese), once you landed here, you were legal.

“Only 1 percent of people who showed up at Ellis Island were turned away,” said Mae Ngai, author of “Impossible Subjects: Illegal Aliens and the Making of Modern America.”

Which brings us to the second reason the “my ancestors came legally” argument is absurd. It’s because lots of people’s ancestors simply didn’t.

Once Congress put immigration quotas in place to keep out less desirable eastern and southern Europeans in 1921, they began sneaking in by the thousands. On June 17, 1923, the New York Times reported that W.H. Husband, commissioner general of immigration, had been trying for two years “to stem the flow of immigrants from central and southern Europe, Africa and Asia that has been leaking across the borders of Mexico and Canada and through the ports of the east and west coasts.”

A story from the Sept. 16, 1927, New York Times describes government plans for stepped-up Coast Guard patrols because thousands of Chinese, Japanese, Greeks, Russians and Italians were landing in Cuba and then hiring smugglers to take them to the United States illegally. Two years earlier, the immigration service reported that 1.4 million immigrants might be living illegally in the U.S., according to the immigration service’s 1925 annual report.

The problem got so bad that the government was forced to legalize an estimated 200,000 illegal European immigrants by a process called pre-examination. These days, the process would be called amnesty.

Clearly, if everyone’s grandparents said they immigrated legally, someone’s grandparents were lying. Stanford University history professor Richard White discovered that after he began researching a book on his family’s immigrant past. White found his grandfather tried to immigrate from Ireland through Canada in 1936 because he could not get a visa under the quota laws.

“He tried to come through Detroit. It was hard to get caught at Detroit, but he managed to get caught,” White said. Back in Canada, his grandfather called his brother, a Chicago police officer, who crossed the border and met him there. The two then walked to Detroit, his brother flashing his Chicago policeman’s badge to U.S. customs officers who waved the pair through.

“I wouldn’t be here, my brothers wouldn’t be here if illegal aliens had been rounded up and dragged out,” said White, a 1992 Pulitzer Prize finalist. Few people say what White does in public. They’re not going on talk shows, blogging or writing letters to newspaper editors. But they’re out there, even if they don’t know it.

Perhaps if the Senate’s legalization bill comes around again, their story could be a rallying cry for those in favor of amnesty.