MEXICO CITY—Influential Mexicans are pushing an aggressive and perhaps risky strategy to fight a likely increase in deportations of their undocumented compatriots in the U.S.: jam U.S. immigration courts in hopes of causing the already overburdened system to break down.

The proposal calls for advertising campaigns advising migrants in the U.S. to take their cases to court and fight deportation if detained. “The backlog in the immigration system is tremendous,” said former Foreign Minister Jorge Castañeda. The idea is to double or triple the backlog, “until Trump desists in this stupid idea,” he added.