Jimmy had been pardoned, and thus got out of jail early, because of his political connections. A state governor is the person who has the power to pardon state prisoners. I guess (but I’m not sure) that the “protest from Springfield” was a protest by somebody against the idea of pardoning Jimmy. To “buck against” the protest means to fight back against it or to resist it. (“Bucking” is what a horse does when it kicks its hind legs of the ground to try to make a rider fall off. So, by extension, it can refer to other kinds of resistance/fighting back). “Balked” means hesitated or stopped. So, the idea appears to be that someone’s protest put political pressure on the governor NOT to pardon Jimmy, and that that protest delayed the pardon (“sorry we couldn’t make it [the pardon] [happen] sooner”) because the governor hesitated, but finally the governor granted the pardon.

Thank you for your comment.

Well they went against a protest, and the governor hesitated when they were supposed to do it. <that’s just a more modern translation of it. I only speak English. Balk: hesitate Buck: resist