They did that in 2006 when Comprehensive Immigration Reform was in preparation and under debate.
They rallied to show their numbers but they carried Mexican flags. When the media showed them with those flags it caused a public backlash. In rallies that followed, they carried little American flags.
YEP!! the Day without an immigrant.
Remember it vividly - a complete SEA of mexican flags at the first rally.
Not so much afterward as the Spanish DJ’s informed them it’s hurting their cause.