It’s the most familiar and most American of stories: The immigrant arrives on these shores with just a few dollars in his pocket and little English or education, but with wits and grit creates a great industry.

It’s a great story about the promise of this nation, and the more penniless the newcomer, the better it is.

This is the story the Trump administration wants to end.

Last week, the White House issued a new rule targeting legal immigrants who want to stay in the United States but whose lack of financial resources are judged likely to make them a burden on taxpayers. It will almost certainly mean accepting fewer people from Latin America, Africa and parts of Asia.

This is of crucial importance to Florida, where some 4 million residents are foreign-born, about one-fifth of the state’s population. Where the most important industries — farming, hospitality, construction — would be crippled without the labor of striving immigrants who arrive here with little but the will to work.

Ken Cuccinelli, acting director of citizenship and immigration services, described the administration’s aims succinctly with a jarring rewrite of the Emma Lazarus poem at the base of the Statue of Liberty.

“Give me your tired and your poor who can stand up on their own two feet and will not become a public charge,” Cuccinelli told an NPR interviewer.

How dare he, this Trump appointee whose own immigrant great-grandfather arrived here penniless through Ellis Island from Italy, a country that then had roughly the same social status as Mexico does now.

Cuccinelli also claimed, in a subsequent CNN interview, that the poem was intended to welcome only European immigrants. Not so. The poem says that from Lady Liberty’s torch “glows world-wide welcome.”

The new rule, a top priority of immigration uber-hard-liner Stephen Miller, is designed to ensure that newcomers don’t use programs such as food stamps, Supplemental Security Income and temporary welfare aid.

According to a study cited by the New York Times, nearly three-quarters of recent arrivals from Mexico and the Caribbean have relatively modest incomes that could make them shaky candidates under the new rules. Immigrants from Europe and Canada are least likely to face problems.

And this idea that immigrants are an enormous burden on the taxpayers? It’s bogus. In Florida, immigrant-led households paid one-fifth of all state and local tax revenues in 2014, according to the advocacy group New American Economy.

Immigrants in Florida paid more than $12 billion into Social Security and Medicare that year. Remember that for immigrants here illegally, that’s money they’ll never collect, since they’re using phony Social Security cards. That’s a gain for Uncle Sam, not a drain.

Yes, the government should fight welfare abuses where it finds them. But no, it must not use the potential of welfare abuse to allow entry only to people of means and to deliberately sculpt the American population to be whiter and less diverse.

The Trump administration must not be allowed to change the American story like this.