San Francisco and the county of Santa Clara, California, on Tuesday filed a joint lawsuit against the Trump administration’s regulation that makes it harder for immigrants to obtain green cards if they’ve received or are likely to receive government benefits.

Since it was announced Monday, the “public charge” rule has been met with fierce backlash from Democrats, immigration advocates and others who argue it will discourage legal immigrants from receiving benefits they’re eligible for.

“By design, it will also coerce thousands of immigrants and their family members to forgo or disenroll from critical federally funded, county-administered programs — even benefits not technically covered by the Final Rule — to reduce the risk that they or their family members will be denied admission or permanent residency,” the complaint filed by Santa Clara County and San Francisco reads, adding that some people have already disenrolled from benefits “out of fear.”

The 837-page rule applies to those seeking to come to or remain in the United States via legal channels and is expected to impact roughly 382,000 people seeking to adjust their immigration, according to the Department of Homeland Security. However, immigration advocates say millions of people could be affected by the regulation.

The lawsuit seeks to block the rule, alleging that counties will incur additional costs due, in part, to residents moving toward services paid for and administered by counties,

“Not only will the counties have to provide support previously furnished by the federal government, without any corresponding allocation of federal funds, they will face the new, increased costs of dealing with harms to public health,” they wrote in their complaint.

Acting US Citizenship and Immigration Services Director Ken Cuccinelli has insisted that the rule will encourage self-sufficiency, and drew criticism Tuesday when he revised the iconic poem on the Statue of Liberty’s pedestal to suggest that only immigrants who can “stand on their own two feet” are welcome in the United States.

The regulation will likely continue to meet legal challenges. New York state Attorney General Letitia James announced Monday evening that she plans to sue to block the rule, saying that under the rule, “children will go hungry; families will go without medical care.”

Rule targeting legal immigrants draws first lawsuit