The Tea Party, while not a "republican" movement, is a "conservative" movement and thus while it encompasses some independent, libertarian and even democratic support its primary national presence in terms of elections is the Republican party. As such I imagine it’ll do what most ideological movements do when their side is placed into office…remain in existence but either be co-opted to remain in existence and keep power and/or move to the back and private channels for their unrest.
In regards to the first part happening, it would depend on whether or not the Republicans that are elected follow the Tea Party model or not. If they don’t, the chance of it being co-opted reduces itself as there is still a purpose for the movement. If they DO however make headway on Tea Party issues then the purpose of the movement is weakened a bit and, as is the case with most ideological political movements, those that seek power will attempt to co-opt it rather than embrace its success. Feminism and the Civil Rights movement are two such examples, rather than progress with recognition of the success those movements have made those that are at the top seek to keep it burning with as much, if not more, fervor then it was at its peak because to present the situation as somehow significantly better then it was would be to purposefully weaken their own foot hold and power. So the first part of the equation is hinged on how successful the Republicans are at pushing the Tea Party Agenda or not.
The second part has little bearing on whether or not the agenda is successful and more to do with human nature. Inherently people are lest app to PUBLICLY rip “their team”. You can see this in sports routinely, where fans will voice unrest concerning issues with the team privately but don’t typically vocally in public bash their team…but have no issue doing so to others. Look too at how people react toward speaking bad against strangers or even acquaintances and friends…but are less apt to do it PUBLICLY about family or very close friends.
In politics, this is in part due to an understanding that as bad as your guy might be on issues you care about there is a good chance that the other guy will be as bad if not worse on those issues AND on other issues you care about as well. So the method of complaining to get the results you wish changes. It’s beneficial to be loud, vocal, and in the spot light about your complaint with the other guy in office because such public negativity tends to do some damage and will help increase the chance of your guy getting in. However, when your guy is in power being extremely vocal, loud, and in the spot light is actually detrimental to your cause. Such acts are typically not significantly more likely to succeed in terms of getting your POLICY pushed than more private, individualized, and back channeled forms of protest. The purpose of loud and showy things is not so much to get your policy pushed but to get attention to your issue and gain VOTER support. As such, doing big protests like that when your guy is in power is actually increasing your chances of doing harm to your goals because it’s more likely to simply increase the chance of getting your guy voted out then it is to get policy changed.
It’s not like the anti-war movement and the immigration movement stopped putting pressure to get their policies enacted when Obama went in the white house. However, save for a portion of those who are single issue voters, they recognize that it is more beneficial in terms of the policies they want to make their push through a different method then they did when Bush was in office. If they continued to make their push in the same fashion the more likely result then getting a BETTER anti-war candidate would be that they’d simply help get a Republican elected who would end up being as bad if not worse on their pet issue AND on other issues they care about.
Similarly, the Tea Party movement will likely undergo a different method of protest and policy pressure if Republicans get elected in 2012. That doesn’t mean they movement won’t still push their issues, but they’ll do so in a different method that gives them the best chance to get the most of their policy enacted.
I personally have no issue or see no hypocrisy on the side of the Anti-War movement or would see it on the Tea Party movement if they acted similarly. It’d be one thing if they came out as a movement going “We support 100% of what the guy in office is doing in regards to our issues” when it’s clear the guy isn’t actually doing that…but that hasn’t happened, and I don’t think it will happen. But I expect an ideological movement to do what is most likely to bring about the most of their policy as is possible…and when the party that matches their ideological side is in office that action is to look towards more discreet methods of political pressure rather than overt. To expect ideological movements on either side to act differently is to expect them to act detrimental to their purposes and to be 100% slaves to ideology.
Most Ideological movements, as is the case with most people, have to balance between ideological principle and ideological practicality. I.E. they have to balance between getting the purest policy possible or getting the most policy possible according to their desires. There are very, VERY few movements that are 100% ideological and 0% practical. There may be individuals within a movement that are of that make up, but few movements as a whole are. The ones that are you almost never hear about because they are SO far out of the mainstream that they have no real relevance.
So to summarize…I think the visible Tea Party influence will appear reduced if the Republicans get elected. I believe the back channel and private political pressure will remain relatively strong IF Republicans fail to follow through on tea party principles once elected. I don’t see any problem with this, or with how other ideological movements have acted, as I believe that such a change of approach is in the best interest of those movements to get the most of what they want done.