Just a few weeks ago, protesters marched through the Michigan Capitol claiming that Republicans were trying to subvert the will of voters and seize power from the Democrats who had just been elected governor, attorney general and secretary of state.

The protesters’ worst fears did not come to fruition.

On Friday, Gov. Rick Snyder, a Republican whose eight-year tenure ends next week, vetoed a bill that would have allowed lawmakers to intervene in court cases, a measure seen as an effort to dilute the authority of the new Democrats. Other legislation that would have stripped power from incoming officials never made it to a floor vote.

The results gave Michigan Democrats some measure of relief, though they were not at all thrilled with what had happened in recent weeks. Mr. Snyder also signed or vetoed dozens of other bills this week passed by lawmakers during their busy, contentious lame-duck session.

“Some of the ones that he vetoed, we are a little surprised that he vetoed,” State Representative Adam Zemke, a Democrat, said. “And so that’s a positive thing.”