No promises were made, but New Haven Mayor John DeStefano seems to think House Speaker Brendan Sharkey gets how bad Gov. Dannel P. Malloy’s budget is for municipalities.

“We have been talking in this building as Democrats and Republicans for 20 years about the problem with the state’s over-dependence on the property tax,” DeStefano said. “And here you’ve got a budget that more than ever makes the state more dependent on property taxes.”

DeStefano and Connecticut Conference of Municipalities Executive Director and CEO James Finley visited with Sharkey on Tuesday afternoon to talk about the way the governor’s budget changes municipal funding formulas. Mayors and First Selectmen have complained that the governor’s budget will force them to increase property taxes. They’re hoping legislative leaders will craft a budget that’s more friendly to municipalities than Malloy’s two-year, $43.8 billion budget.

“In the meantime, do no harm,” DeStefano said.

So is Malloy’s budget the worst he’s ever seen in his 19 years as mayor of the Elm City?

“Let me be very clear, I have never had a budget that increases taxes in New Haven by 4-and-a-half mills from the state. That’s true,” DeStefano said in between meetings with Sharkey and Sen. President Donald Williams.

“I think that there’s an acknowledgment in this building that the governor’s approach is not the right way to go,” Finley said.

DeStefano said the visit was an effort to lobby legislative leaders to come up with a different budget than the one Malloy released on Feb. 6.

Last month, DeStefano and other big city mayors held a press conference to call Malloy’s budget a “shell game.”

Malloy has maintained that his budget places a higher priority on education funding and sends more money to municipalities.