President Reagan's pledge to speed up the execution of the Department of Energy to aid his budget battle ran into opposition yesterday from liberal Democrats in the House who said the administration is courting a constitutional fight if it dismantles programs Congress wants saved.

Taking his cue from President Reagan's speech Thursday, Energy Secretary James Edwards told reporters yesterday he will try to have a plan for abolishing the DOE prepared by the end of November, more than a month ahead of the original schedule.

Edwards said that well before the DOE is dismantled, he intends to continue deep cuts in his department's programs and personnel. He hopes to have DOE spending pared from the $16 billion total in the Carter administration's fiscal 1982 budget to less than $12 billion in fiscal 1983, which begins a year from now. Another $2 billion should be cut by fiscal 1984, he said.

But he had no word on how far administration budget officials want to go in reducing or eliminating current investment tax credits for residential and commercial investments in solar and other alternative-energy equipment. Edwards says he supports these programs, but the White House says they are being reviewed.

House liberals were building a backfire against these actions yesterday, summoning DOE officials to a hearing to explain personnel cuts in conservation and enforcement programs that Congress still supports.

"It appears this administration has chosen to flout its constitutional mandate to execute the laws, not make them," said Rep. Richard L. Ottinger, chairman of the subcommittee on energy conservation and power of the House Energy and Commerce Committee.

The argument yesterday dealt with personnel cutbacks in the 1981 fiscal year, which ends next Wednesday.

The larger issue is how tightly the DOE is bound to obey preliminary congressional action on the fiscal 1982 budget. Edwards told Congress this week that the DOE is proceeding with cutbacks in programs and personnel according to administration plans. If there is a significant change in plans, when Congress and the president finally agree on the 1982 budget, the DOE will respond accordingly, he said. "The option of adding staff is always available," Edwards said in a letter to Rep. John Dingell (D-Mich.), chairman of the House subcommittee on oversight and investigations.

Dingell and Ottinger headed a joint subcommittee meeting yesterday on DOE personnel cuts, and Dingell echoed Ottinger's attack on them.

And Rep. Albert Gore Jr. (D-Tenn.) predicted that the House will not go along with Reagan's plan to dismantle the DOE. "The energy crisis is not over," he said, warning against a "false sense of calm" brought on by the current surplus in energy stocks.

In his interview with reporters, Edwards said that wasn't an issue. "I never said the energy crisis was over," he said. But the administration is convinced that government energy regulation makes the situation worse, in both times of calm and crisis.

He said that he and top aides have just begun a study of how the department should be dismantled and where the programs that will survive should be placed.

The nuclear weapons program, which accounts for about $5 billion of the DOE budget, is "too important to leave in the hands of the admirals and generals," Edwards said. He leans toward creation of a federal agency to handle all federal nuclear activities