While there may be talk about the improved working relations between the Board of Supervisors and the mayor, it’s going to take more than good vibes to solve The City’s $383.4 million budget deficit for the fiscal year beginning July 1. That’s the deficit projection as of Wednesday.

Even if The City cut across city departments’ budgets by 20 percent, and implemented an additional $70 million in identified savings — including a $30 million reduction in capital spending — The City’s deficit would be at $120 million. And that doesn’t factor in potential changes in the state cuts.

Also, some city departments will not be able to reduce their budgets by 20 percent, according to Mayor Ed Lee’s budget director, Greg Wagner.

“We got a big issue in front of us. We’re going to have a lot of work to do to try and figure out ideas about how to close this. And we got a short time frame to do this,” Wagner said.

City departments submitted their proposed budgets for next year on Tuesday for review by the Mayor’s Office. The budget proposals include 10 percent in cuts, and an additional 10 percent in contingency cuts.

The mayor is charged with submitting a balanced city budget to the board for review and adoption by June 1.

jsabatini@sfexaminer.com