The worst that can happen is the church will lose its tax-free status. Some would say, myself included, that this would be a good thing. Now the pastor is truly free to preach the whole Word of God without any government restrictions. He could back any candidate he wanted to and even name names. They may have to cut a program or two because of a tighter budget, though.
I think this is the whole point of this pastor challenge. Under the First Amendment the government does not have the right to tax (to tax is to regulate behavior) the church. This would mean that the government may not take away a church's exempt status because the church is not subject to tax in the first place.
I believe I've already read that in some places that pastors cannot condemn homosexual behavior because it is "Hate Speech". This is an effort to manipulate the inner workings of the church to conform with the liberal agenda.
If this group can afford the lawyers, there's no way the IRS will allow the case to go to court - because they'd lose.