Democrats won big in Tuesday's elections, coming out on top in several heavily contested ballot measures on an anti-union law in Ohio and an abortion-related amendment to the Mississippi constitution.

Voters rejected what Democrats called Republican overreach in pushing extreme policies once they were swept into office in the GOP tide last year.

If you overreach, the people will respond, Ohio Democratic Chairman Chris Redfern said Tuesday night.

Ohio Restores Collective Bargaining

In Ohio, the perennial bell weather in presidential elections, an anti-union law that curbed collective bargaining was soundly defeated at the polls by a nearly 2-1 margin. Known as SB5, the law was a central component of Gov. John Kasich's agenda.

Meanwhile, in Mississippi, voters overwhelmingly rejected a proposed constitutional amendment defining personhood as beginning at the time of fertilization.

The measure was intended to outlaw abortion in the state, but the ballot language prevented abortion-rights opponents from fully supporting the amendment. Also, the amendment's effect on birth control entered the debate, shifting the focus off abortion.

Even Mississippi Gov. Haley Barbour, a Republican who said he believes life begins at conception, said he was concerned about the ballot measure's language.

Democrats also came out on top in state races, sweeping nearly every statewide office in Kentucky, where Gov. Steve Beshear routed his GOP opponent to handily win a second term.

Inside statehouses, Democrats held onto an Iowa state Senate seat that let them hold onto their thin majority, though the party has a tenuous grasp in the Virginia Senate.

There is one outstanding state Senate race in Virginia that will determine control of the chamber. If Democrats prevail, they will prevent a Republican takeover of state offices in Virginia, a key battleground state in the 2012 elections

Big City Mayoral Races

Big city mayors also had a great election night as incumbents were reelected in Philadelphia, Baltimore, and Charlotte, N.C., among other cities despite a weak economy and austerity at the state-level. Voters in eight cities among the largest 25 went to the polls Tuesday.

In San Francisco, Mayor Ed Lee is expected to win a full-term after he was appointed on an interim basis to take over for Gavin Newsom, who had been elected California's lieutenant governor. Lee will be the city's first elected Chinese American mayor once results are finalized.

Phoenix will get a new mayor as Democrat Greg Stanton, a former city Councilman, defeated his Republican opponent Tuesday evening.