SPRINGFIELD — Of the nearly two dozen new legislators sworn in at the Capitol this week, a handful are lawyers looking to make their mark in a tough political climate.An unprecedented budget stalemate, catalyzed by the ongoing political war between Democratic legislative leaders and the Republican governor, make it a difficult time to take the oath of office.But the new lawyer-lawmakers say they’re up for the challenge — and even optimistic.“I’m very hopeful. I think there is a lot of turnover …