Trump stands a chance but if he fires Mueller he's toast.
I'd like to think so, but frankly he fired Comey for the same thing and he got away with it. He's declined to state whether he'll pardon Flynn (Why on earth would he pardon Flynn?). He wants the Russia investigation to stop. The more he protests, the more obvious it becomes that the investigation is leading to his door.
These aren't the actions of an innocent man. An innocent man would by default respect the judicial process and the law behind it that is the very basis of his Presidency, and let the investigation run its course. Now if Mueller couldn't stop tweeting every five minutes about how all conservatives are corrupt etc, then a sensible person would question Mueller's objectivity. But there's basically no reason to question Mueller's objectivity, judging by (public) appearance he's keeping his head down and knuckling down to the job he's been given.
If Trump does manage to fire Mueller, then it's the politicians' job to hold Trump accountable for impeding an investigation into the highest levels of government, and its the peoples' job to start protesting Trump's actions because it's a threat to a healthy democracy. If the people and the politicians fail to do their jobs, then I think a coup in the US starts to become a very real possibility, because if the President can basically do whatever he likes without any checks and balances, then the US may as well give up on the idea of democracy and hand Trump's family all the keys to the kingdom, and Trump can tell the people about how much money he's saved by firing everyone in the senate and congress.