Support of the people reads: " After you win a power challenge by 5 or more STR, search your deck for a location with printed cost 3 or lower, and put it into play. Shuffle your deck. (Max 1 per challenge.)"
While Limited means: " A player may not marshal or play more than 1 limited card each round, or place more than 1 limited card during setup."
If you have already marshalled a limited card in this round, can you put another limited card with the effect of support of the people into play?
It's essentially "put [a card] into play" vs "play [a card]"