I have written a Star Wars EU FOTJ political meta.
Because...I don't know, really. I blame
King, Kaiser, Tsar, which I just finished & which did a fantastic job of describing the political build up to WWI.
And so now I'm like "how does this apply to FOTJ?" Because I am a DORK.
The GA has just come through the Galactic Civil War as the aggressor. It's lost money, men, and lots of prestige.
Assuming that Jacen's alterations to GA law haven't been repealed, the Chief of State retains immense, unchecked powers. It's possible that the GA may have been forced to pay restitution to worlds like Kashyyyk and Fondor.
If the spoilers from Outcast are any indication, Daala has kept peace for two years, and now she's getting down to business. It appears she's retained the GAG (and possibly supplemented them with Mandos) and has set her sights firmly on discrediting and destroying the Jedi Order. Galactically, it appears to be a good time for it; people are sick of war and not looking to get in to another one just for the Jedi (Who, despite being pulled from every world, are very much a minority). And the Jedi's allies aren't in much of a position to help.
Hapan Queen Mother Tenel Ka is a Jedi and (more importantly) sees herself as one. This should make her a natural ally and defender of the Order. Unfortunately, her relationship with fellow Jedi Jacen Solo also dragged Hapes in to the war--right before the heir to the Hapan throne was "killed". Tenel Ka may be an all-powerful Queen, but Hapes is a dog-eat-dog place. She's going to have to fight her nobles and risk assasination if she wants to try to help the Jedi, and without her father or child to continue her rule, she's exceedingly vulnerable. It's extremely doubtful that Tenel Ka could challenge the GA if Daala took aim on the Jedi--at least, not now. According to Outcast, Hapes has yet to rejoin the GA--while Tenel Ka could try & leverage this for Jedi safety and/or survival, it's again taking a rather large risk. Daala could easily reject her terms and rally the GA against the Jedi AND Hapes--ruled by a Jedi Queen.
The Empire is now under the rule of Jagged Fel--but he's pretty much alone there. He was promoted to his position by the Jedi Grand Master and has absolutely no support structure there. He's canny enough to have developed some alliances in the intervening two years, but the Moffs have never been particularly troubled in matters of loyalty. If the Moffs see an opportunity to remove him, they're going to take it. So while Jag may be a big fan of the Jedi (and in Outcast he's lobbying quite hard for a Jedi presence within the Remnant), he can't exactly stick his neck out for them. It would be far too easy for the Moffs to use this against him to discredit and unseat him--this man who was appointed to command of the Empire by a Jedi and whose lover is a Jedi (Jag points out in Outcast that Jedi have become 'bogeymen' within the Empire since Palpatine's death...this is not a government to come to the aid of Jedi). Hapes isn't likely to ally with the Empire, either, though they could unite against the GA, because of the Moffs' "murder" of Princess Allana.
Corellia is exceedingly proud of its natives sons: Han Solo (who's pretty much "Father of the Jedi" at this point), Wedge Antilles, Corran Horn (whose son goes psychotic & prompts the GA moves against the Jedi)... these are men who aren't going to stand for action against the Jedi and may be able to pull some Corellian muscle in to the fight. But the legitimate Corellian government isn't going to be able to do much. Corellia suffered during the war; she was blockaded, lost Centerpoint (which may, depending on how things work within SW, have a dramatic impact on all of the Five Worlds), and waged an expensive war against the GA in which Tralus was bombarded and occupied. Their economy has to be hurting. Add to the fact that Corellia spent part of the war under attack by the Jedi, and are likely to be more concerned with their own problems than those of some Force-users in the Core.
The Chiss are a wildcard here. Frankly, they rarely get involved--it took the threat of galactic extinction from the Vong to get them in to the Known Regions before, and they were AWOL during the Second Galactic Civil War. Of course, the Chiss are old-school Imperial allies (Grand Admiral Thrawn), and a *supposedly* exiled Jag Fel is now steering Imperial politics. Baron Fel is probably still an important guy among the Chiss; it's possible that the two could ally against a greater threat. BUT...Jag's (apparently) on the outs, his father's not exactly one of the ruling families, and the Jedi are known to the Chiss as Killik sympathizers thanks to the Dark Nest Trilogy.
HOWEVER: while the Empire may not be able to go to WAR over the Jedi, it might just be possible for Jedi to refugee there. Part of Jaina's refusal to start an "offshoot" of the Jedi within the Empire is because she's the Sword and is meant to defend the Order. If the Jedi have to get out of the GA, lots of them will probably head to Hapan space, where the training facility is (according to Jag in Outcast). But Jag would definitely welcome Jaina (and I think this would be a reasonable opportunity for Jaina to feel like she's doing her duty while being with Jag) and might be able to spin the presence of Jedi within the Empire to his advantage; after all, if the GA's kicked the Jedi out, the Empire would be one of those few governments with official Jedi presence & assistance.