Treasury Secretary Donald T. Regan said yesterday he thinks the Democratic-controlled House will pass the administration's economic program during a showdown on Capitol Hill this week.

Regan also said he had "reasonable assurances" that three Republicans who doubt the administration's plans will fall in line after they are shown new figures on the plan today.

Regan said, "We think we will be successful in carrying Gramm-Latta," a version of the administration's plan sponsored by Rep. Phil Gramm (D-Tex.) and Rep. Delbert L. Latta (R-Ohio). But Regan said he didn't know exactly how the vote will go since the House Democrats have their own proposal. "It is close," Regan said. "Every vote will count."

One vote indicator is the number of Republicans and Democrats in the House, Regan said. But he added, until Congress returns from its Easter recess this week, he can't predict how the vote will go.

Regan also said the momentum of the economic program hasn't been slowed because the president has been recuperating from gunshot wound instead of conducting extensive compaigning for the plan. The administration's hopes are stronger now than before the Easter recess because congressmen have been able to go to their home districts and listen to constituents who want the Regan plan, Regan said.

When President Reagan addresses Congress Tuesday, he will say "it's time for action" and that he wants to cooperate, not compromise on his economic proposals, Regan said.