The pressure from some immigrant activists to reject any compromise that would tighten border security has frustrated Democratic leaders, who recognize the political risks of being labeled the party of open borders — a potentially lethal tag as they seek to regain support from working-class voters across the Midwest.

Fearful of concessions to Mr. Trump that could increase immigration enforcement aimed at their families and friends, the activists are targeting Democratic congressional leaders with loud political protests. And Democratic politicians may be vulnerable. They have already shifted to the left on a number of issues, such as health care, as they try to take advantage of liberal fervor stoked by the Trump era.

But moving too far to the left on border security could hold serious risks for a party that lost the presidency with defeats in Pennsylvania, Wisconsin, Michigan and Iowa — all states where immigration remains a hot-button issue.