Depends on the incentive. Paying them to go? Nah. We need to change the culture of the tournament within the American hockey community going forward. Hopefully the NTDP will help that as quite a few of the American NHLers have grown up within the USA Hockey national team system. American hockey players just don't grow up with this tournament. They don't grow up watching it. They don't grow up hearing about it. They don't grow up following it. They don't dream of playing in it. Until recently this tournament didn't get much more than small tidbits released, typically either AP press releases or team bloggers mentioning in passing how their player may be doing.
So with that you get American players turning this tournament down without even thinking twice. Granted, sometimes it's understandable (ex: Parise this year trying to come back from a knee injury as an impending RFA). A lot of times it's just because they don't value the tournament enough to put off getting their summer started or doing other things, like R.J. Umberger last year passing so he could take a class or two at Ohio St. It's almost certain that American players won't participate if they're without a contract and injured in any fashion, even small nagging injuries. You don't have those hurdles for the European players that grow up dreaming of playing in this tournament. As such, they'll play injured and play before signing a new contract, etc.
Canada faces similar issues but just don't nearly to the degree USA Hockey does for a few reasons. The obvious, hockey is just that much more popular and ingrained in Canadian culture. It means more. The tournament gets a lot more exposure in Canada and the country cares a lot more. Hockey Canada can use this tournament as a "tryout" phase for players if they want to keep in line for potential Olympic/World Cup teams. They have the depth to tell a player or two to piss off if they don't want to bother representing their country. Brian Burke tried to use this "threat" the year before the Olympics and players still turned down their offers and we don't have the depth to hold that against them. To go along with the depth, Canada can handle a bunch of declined offers more so than any other country and still send a great team.
There's a few things I think need to happen. One is taking place this year and that's increased exposure of the tournament with Versus airing all the USA games. It's going to increase the accountability. Now if we perform like we did last year it may not matter as they're going to have a tough time convincing Versus to continually air the tournament going forward if that happens. Another thing is a breakthrough performance, such as winning the Gold or at least making it to the championship game. It'll attract attention, not only from the hockey community but from other American players. We've missed out on a couple medals in the last few years. We need to string together some success in spite of not having the rosters we'd necessarily like. Another is just continue to grow the sport and produce more hockey players and increase our depth and player pool. Lastly, and it's tough to say here because I don't know the inner workings of the recruitment process but if we have another down roster again, I'd say we need to reevaluate the way we're targeting, recruiting, and selecting our team. Just because the first few offers are declined doesn't necessarily mean we need to start scooping up the Ryan Carters, Colin Stuarts, and Christian Hansons of the world just to put warm bodies in those slots. I don't think that helps further recruitment. Yes, if you offer a guy and he sees the Carters, Hansons, and Stuarts of the world there, he may see an opportunity for more playing time than expected. But the guys that go want to win, too, and you're not going to do it with that caliber of player infesting your lineup. I'd much prefer to see them target some European based players at first if they're getting declined offers over fringe NHL scrubs. Along with that, we seem to fill up our roster too quickly. I'd much rather take 3 full lines and 2 goalies with the potential to add some good players down the line than fill those extra spots with nobodies that will barely play and won't contribute. We may have to take that risk of not fielding a completely full team in the hopes of getting some better talent after the playoffs start.