For store on calypso, "new" orders are any in 'pending', 'processing', or 'on-hold'. If I want to get those orders via the API, I can't do it in one request - currently status only accepts a single status string, or 'any', but no (apparent) way to request a subset of statuses.
One solution would be to pass in a list of statuses, status[]=pending&status[]=processing&status[]=on-hold, and returning all orders that match one of those. This would be useful for other combined status listings, like if we wanted to include completed, cancelled (and refunded?) orders in a list of "finished" orders.
Another solution would be to allow the API to accept status=new, and behind the scenes translate that to [ pending, processing, on-hold ]. If wc extensions can add custom statuses, this might be better so they can indicate if some new status should be considered "new".