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]"

Yes. It's a put into play effect, which Limited doesn't interact with in any way (see RR p12 "xxLimited cards that are “put into play” via card effects ignore and are ignored by this restriction.").

Note that currently there are *no* limited cards that are 'played' (only events are played); only marshalled or placed in setup.