Americans strongly back giving illegal immigrant “Dreamers” a pathway to citizenship — but a new poll found they also strongly back the other changes President Trump is pushing to build a border wall system, eliminate the visa lottery and curtail the chain of family migration.

The Harvard-Harris Poll, taken in the run-up to the government shutdown, even found huge support for cutting the level of legal immigration, which stands at more than 1 million a year, to less than half that.

The findings challenge the Gang of Six immigration deal Democrats and some Republicans tried to push through the Senate last week, only to see their efforts derailed by Mr. Trump.

That plan, authored by Sens. Lindsey Graham, a Republican, and Richard Durbin, a Democrat, called for a generous legalization for Dreamers, a small downpayment on Mr. Trump’s border wall and no significant changes to chain migration. The plan would have eliminated the visa lottery, but pumped those visas back into the legal immigration system to be used for a new amnesty for people from countries that suffered natural disasters.

Mr. Graham over the weekend said senators will never accept a deal that cuts the overall level of immigration, but the new poll says that’s exactly what Americans want.

The survey asked respondents what number they would like to see. A stunning 35 percent said legal immigration should be 250,000 a year or less, while another 19 percent said it should be between 250,000 and 500,000. Combined, they make up a majority looking for a cut of at least 50 percent over current annual levels. Another 18 percent said they want to see between 500,000 and 1 million.

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