With supermajorities, Democratic lawmakers have historic new powers.

They could raise taxes, while Republicans sit on the sidelines.

CONWAY: "Well I used to be on the sidelines, I was a cheerleader."

That's Assembly Republican leader Connie Conway, joking. She says Republicans are not on the sidelines, they will work with Democrats when the Democrats have trouble reaching consensus.

And Republicans might also find an ally in Democratic Governor Jerry Brown, especially if he continues to maintain tight control of spending.

CONWAY: "I think the Governor should look to us for help and support, as we feel we have been a help and support to the Governor since he got here after all with his pension reform bills, Republicans put that forward and were driving and pushing that issue."

Republicans do have their own agenda.

One piece of legislation they've introduced would freeze tuition at state colleges and universities for seven years while the Proposition 30 tax increases are in effect.