There's absolutely no way that Google can launch the next Nexus at $350, or even $399 (I'd flip if they did). With the small scale production runs they'll be making (the Nexus traditionally isn't the biggest seller ever), they just can't cut costs and get it down to those price points at the start.
We don't have a ton of prior info on this because there have only been 2 previous Nexus phones, only one of which sold directly by Google. The Nexus One sold at $549 if I recall correctly (directly from Google), and the unlocked T-Mobile version of the Nexus S sold for $529 via Best Buy at launch.
If Google is going to be aggressive, and considering the cost of the Nexus 7 they probably will be, we can hope for maybe $449... more likely in the $499 - $549 range based on their previous pricing. I think I'd be happy with that still, as it well undercuts the cost of most unlocked phones, which go for $600+ and when the Galaxy Nexus went on sale late last year, being offered through importers, people were paying $700+ for it. I paid $550 and that was after waiting until late January for the price to come down.
Only time will tell, and I surely hope that selling it directly in the Play Store at launch will help keep the prices down.