In certain respects, this is kind of crazy. Christie is pretty conservative, especially for a blue state governor, he is really popular, and he is a good public speaker who can bring the kind of fiery rhetoric that partisans like. At the same time though, Christie's positions completely undermine the conservative agenda. And for that reason it makes sense that they won't invite him.
Conservatives have been demanding major cuts to non-military, domestic spending, and any plan based on these types of cuts (like the"Ryan Plan") require FEMA to drastically reduce their operating budgets. This position only make sense if you think the country is better off without the federal emergency assistance provided by FEMA. By publicly calling for federal aid, Christie exposes the weakness of this position--in times of crisis, States do need the federal government to help out.
A similar problem exists surronding his comments about Obama. Republicans have entered into the negotiations over the debt ceiling, fiscal cliff, and sequester with positions that are far less popular than Obama's. In order, to compensate for this, they have been claiming--with the assistance of some beltway reporters-- that Obama is an unfair negotiator, who is unreasonable and difficult to work with. This has been moderately effective because it is very hard to disprove. What does disprove it though, is Christie saying that he is great to work with!
In the next few years, conservatives are going to have to moderate their positions on social issues. Gay marriage is becoming more popular, and their more extreme positions on abortion are costing them senate seats. At the same time, they are trying to move to the center on immigration, and are still uncomfortable with unilaterally calling for cuts to entitlements. What's left? non-military domestic spending, and Obama's intransigence over it. Christie is subtly undermining both of those positions.