It was one of the first times the Democrat-controlled legislature publicly disagreed with Gov. Dannel P. Malloy, but its decision Tuesday to change how federal heating assistance is distributed to low income families didn’t seem to faze the governor.

“It’s a process,” Malloy said Wednesday. And as part of that process the Malloy administration has to present its plan first.

The Malloy administration proposed spending an estimated $46.4 million in federal heating assistance on homes heated with “deliverable” fuel. The decision meant low income residents who use gas or electric to heat their homes and apartments wouldn’t receive any assistance. The Malloy administration had reasoned that utilities are barred from shutting off gas and electric customers during the winter.

But many who testified at Tuesday’s public hearing said it doesn’t mean they wouldn’t face a possible shut off in May, if they were unable to pay the bill, which would continue despite the shut off moratorium.

“It was a very good plan to make sure no one would go without heat during the winter,” Malloy said.

A trio of legislative committees Tuesday didn’t believe Malloy’s plan was fair so they changed the formula to distribute a maximum of $255 to some of the poorest households and increased the amount of money the state expects to receive by about $15.22 million.

The state will be on the hook to find the additional $15.22 million in its own budget if the federal government doesn’t give lawmakers all the money they expected.

Malloy said his plan “limited state exposure financially.”

“I think we can easily predict that that money is the most vulnerable in deliberations that are going to take place this year and the coming year in Washington,” Malloy said.

Meanwhile, “it’s a big budget,” Malloy said. “We’ll work with folks of good will.”

Rep. Vickie Nardello, co-chairwoman of the Energy and Technology Committee, said they recognize by adopting the legislature’s plan to spend $61.6 million is beyond the $46 million the president proposed. However, she said the U.S. Senate plan would send Connecticut $76 million. She said over the past 10 years the president’s proposal was never adopted.

But a with a House controlled by fiscal conservatives, Malloy’s Budget Director Ben Barnes, said he’s nervous that increased funding will reach the state.