Ha ha... Their chances aren't good.
You see, the problem with rebelling against the king while having 6 months is that there's a good chance money won't save you, let's look at this from certain aspects that tie in directly with economic factors:
Military. You rebelled against the king and did things that will get him, all of his nobles and all of their noble's vassals against you. Not because you're taking the king's land, but because you preemptively attacked nearby nobles and is clearly agaisn the system they run. In other words, you're a threat (especially for the nearby nobles) and needs to be trampled ASAP to ensure stability to the system. This means that the chances of the king not being able to gather a decent military force will likely depend more on whether the nobles have decided they didn't need armies for any reason than on nobles not joining in, because you've shown every member of nobility you might go for them next if you feel like it. Furthermore, you have 6 months to basically build an army from the ground, your townsfolk and the peasants. Money isn't the problem here, time is. Proper military forces take time to train, especially regarding more elite positions such as experienced bowmen and professional knights (both of which were normally trained from a young age), required both a grater sum of money and many more years of training to be made than your "disposable" peasant Frontline soldier (which is also why loosing a bowman or a knight was normally bad, they're not easily replaceable and chances are you can get a ransom for them, at least regarding the knights). Your best bet now is finding trained mercenaries to make a private army, much like kings started doing near the end of the medieval period. If mercenaries are not an option, you'll have to stick to guerilla tactics to have any chance, because it'll be a bunch of poorly trained soldiers against a larger, more well trained opposing army that likely doesn't plan on leaving survivors.
Political. You know how the stock market can fall in a country experiencing internal turmoil? Same here. The king and his nobles may need 6 months to assemble their forces, but letting their territories know that anyone who trades with the rebels will be banished at best and hanged at worst takes a lot less time. Merchant guilds might avoid trading with your city now, because there's a decent chance they'll face retaliation from nearby kingdoms, both physically and economically speaking. If the nearby regions aren't ruled by idiots or stereotypical evil movie nobles with only half a functional brain thanks to inbreeding, there's a chance they'll try to use their political, military and economic power to begin strangling the city before engaging it. Napoleon did it to England (or tried), the nazis did it to Leningrad, the lost goes on.
Social. There's a good chance your city will rely on peasants in a way or another, because trading will most likely be affected and nobody unwilling to piss the king and the nobles off will want to associate with your city. Come in the peasants: as far as your description goes, it doesn't seem like the peasants had a lot of participation in it. As far as it might seem, you're rebelling against the king and nobles and trying to drag them into the hole with you. There's also the problem that sure, they'll live rent free an only be bothered when they need help with construction or military matters, such as right now, right after you've began taking down the nobles, which is the only reason you need them to help you out anyway. Furthermore, unless you show them your well paid mercenary army chances are that all they'll see is a prideful city trying to rebel against the nobles and the king and asking them to join their fragile cause and lack of military power to back it up.
Religion. The entire situation becomes extra bad if your medieval world has similar relations with religion, because the church stands even atop the nobles since nobody wants to go to hell. In such a scenario, if the priests don't side with your rebellion and say you're being controlled by the devil, chances are that neither will the peasants, especially if you respond to such words by doing to the priests what you did to the nobles. Now the city would have reduced trading, reduced food availability, every member of nobility out to get them and a mob of angry peasants trying to end them.
Security. Remember why feudal relationships came to be in the first place? With how invasions and pillaging were happening left and right? Well if your world also has that you'll need to worry with yet another problem, and the existence of such invasions would make proving to the peasants you can protect them as well as the previous nobles even more important, because everyone wants to go to heaven, but nobody wants to die unless there's something in it for them in the afterlife.
So summing up, here are the problems I see as most important:
you've angered the system itself with your actions and will most likely be outnumbered (don't believe me, see French revolution an how every other absolutist country wanted it to be over).
you have very little time to train an effective military force by medieval standards, even through can't depend on a victory through sheer numbers, and you might have to use a good portion of the money to pay mercenaries to fight for you while convincing them that trampling you, stealing your gold and handing over the region back to the old nobles instead isn't a better business (remember, Mercenaries fight for money, and depending on their morality money will be important to ensure they'll remain reliable).
trading might be affected since you're now most likely marked as rebels by the majority of the big figures (and the respective regions) nearby.
you still need peasants to believe your revolution will be better for them than the old system while proving you're still just as capable of offering the same benefits the older system did, such as protection.
if religion is an important part of their lives, especially in case of the peasants, you'll need every nearby priest on your side to prevent revolts from the peasants, and if religion doesn't side with you trying to use force on them will likely make the situation even worse.
if invasions are a thing, there's a chance that you will need to be capable of dealing with them and5 the king's forces.
there's a risk that the king and his nobles will send assassins to get rid of the leaders in the meantime.
All of these affect the economy, because depending on how the peasants, the church, the nobility and the traders see and treat you, you'll need more or less money to make it work, with a worst case scenario where not even all of the money might not be enough to solve the situation in a favorable way for the rebels.