No need to increase production. Contrary to popular belief among Nintendo fans, demand will likely drop slightly sometime between spring and summer, allowing for stockpiling in preparation for the holiday season.
That simply means weekly sales have to drop under 450k units per week to allow for excess stock relative to rate of production.
The official word from Nintendo is that they will maintain production at 1.8 million units until demand subsides. That's from the mouth of Nintendo's Senior VP George Harrison.
Unless you're privy to some information he isn't, or until Nintendo releases information suggesting otherwise, production is 1.8 million/month. End of story.