Rep. Herbert E. Harris II (D-Va.), whose Northern Virginia constituents are "up in arms about heating bills and uneasy over the coming winter," went to the White House yesterday to urge President Carter "to hang tough" in behalf of a consumer-oriented energy program.

Harris was one of 20 House Democrats, mostly young and liberal, who met for 30 minutes with Carter, Vice President Mondale and James R. Schlesinger, the President's energy secretary.

Harris said he urged support for three priorities in the energy bill now being threshed out by a Senator-House conference committee: no deregulation of natural gas prices; a single price for intra- and interstate oil; and a maximum increase of $1.75 per thousand cubic feet for new gas.

The second-term Democrat from Virginia's Eighth Congressional District (Alexandria and southern Fairfax, northern Stafford and Prince William counties) described the congressional delegation as "a tough group, holding tight for a consumer energy bill."

Harris said he came away from the meeting "assured that the President won't authorize any comprosmise with the Senate" without first notifying his House supporters.

"Deregulation of natural gas is just not negotiable," Harris said the President was told. "If that's in the bill, I would vote against it," said Harris. Several other representatives who were with him concurred.

Harris said Carter agreed with them that it is "absolutely essential" that the federal government regulate the total natural gas supply in the nation. The price of gas produced and sold within the bounds of a single state is not now regulated by the U.S.

As a result, Harris said, oil and gas producers in such states as Texas and Louisiana get higher prices for their fuel by selling within their borders, creating shortages in energy-consuming states such as Virginia.

"The President understands the economic distortion two prices can cause," Harris said. With a single price for natural gas, "consuming (nonproducing) states will no longer be at a disadvantage."

While Harris and othe members of the delegation believe there is "room for compromise," Harris said, "there is no question the Senate went completely the industry route."

But the industry "will be better off with this bill (as proposed by Carter and passed by the House) than with the status quo," Harris said.

As the congressmen sipped coffee around the large oval table in the Cabinet room, the President told them he senses "growing support among the public" for his version of an energy program.

His administration continues to "maintain the closest allegiance to the program put to Congress last spring," the President said, and Harris, sitting across the table, nodded in agreement.

An aide to Harris said it was Harris' sixth visit to the White House since Carter became President.