I predict Lucas Giolito will sign with the Nationals. I predict he will sign for well over his slot value, which is supposed to be about $2.1m. I won't be surprised if he signs for $4m, and I don't think the Nats will care that they lost their pick next season.
Edit: Everything below is probably wrong, I've discovered. The reason is that a team who fails to sign a player drafted in round 1, 2, or 3 still receives a compensation pick. Hence, for example, the Nats would have two first round picks next year if they failed to sign Giolito. Likewise, the M's would still have one 1st round draft pick next year if they failed to sign Zunino.
Let's assume Giolito, who may be the best prep righty in the history of the draft, says he won't sign for less than $4m. If the Nats pay it, they will lose next season's first round pick. If they don't, they will lose this season's first round pick. Without injury, Giolito is easily a $4m talent. The Nats will probably pick around 25th next season. No talent even close to Giolito's will be available at that slot.
Thus, that Nats may either (1) give up this season's first round pick or (2) give up next season's pick.* If I'm Mike Rizzo, this is an absolute no brainer: Given the choice between being able to invest $4m in my team's future and $1m in my team's future, I'm investing the $4m, especially in the new system that tries very hard to prevent me from making this sort of investment. Rizzo has a once in a decade opportunity to make an investment in his team at a very small opportunity cost.
And that's why the new system is broken: teams that are winning a given year but have a high value draftee should just kick that draftee as much as they can afford within the confines of the tax that going more than 15% over impose and punt next season's pick. The value of draft picks is thus skewed in favor of winning teams which is antithetical to competitive balance.
Selig and the rest of baseball are going to see this once the Nats announce that they went way over slot to get Giolito. When Bud and Mike chat about it, Bud is going to realize that the system doesn't work.
The Mariners may be in a similar, but less dramatic, situation. That may explain why they're currently on pace to blow their draft cap. If you think you will have to blow your cap to get this year's picks and you think this year's picks are better than what you'll get next year, you should blow your cap this year. The difference is that the M's should expect to draft fairly high again next year (sigh) and so it's less clear that overspending to get Zunino will make sense.
(Please note that the $4m figure I cooked up was for illustrative purposes. I haven't done the math to figure out when the Nationals will pay $2 for every dollar they pay to the player, nor do I know where the Nationals budget is, nor do I know exactly what sort of dollar figure an injury-risk top-talent prep righty should command. $4m was my gut number, and I'm not in any way committed to it from an analytical perspective.)
*Of course, if you can stay within this season's pool, that's best. But there's a good chance that the Nats can't stay in their pool and sign Giolito. They're my favorite National League team, and I'm all for seeing them break next year's bank to get him.