The congressional budget process ground to a halt yesterday as members of both House and Senate impatiently waited for the Reagan administration to declare itself on new budget cuts and tax increases.

"I think it is wrong to say they are sending out signals clearly on anything," Sen. Pete V. Domenici (R-N.M.), chairman of the budget committee, said as he announced that the panel would not take up the second budget resolution today as scheduled.

Domenici, in the current policy dispute within the party, is aligned with David A. Stockman, director of the Office of Management and Budget, in what appears to be an uphill struggle to increase taxes sharply to reduce the large projected deficits over the next several years.

Earlier in the day, the New Mexico Republican met with his principal adversary, Treasury Secretary Donald T. Regan, who argued strenuously against raising taxes. "Right now we are in a down period in the economy. This is not the right time to raise taxes," Regan said after the meeting.

Asked if the president supports his view, Regan said "he's getting shades of opinion," although several participants have said the president will come down on the side of his treasury secretary.

Domenici, in contrast, is pressing his GOP colleagues to accept a three-year program of $199 billion in new budget cuts and tax increases. Of this amount, $84 billion would be new taxes to be imposed over the next three years. In another controversial element of the plan, $27 billion would be cut from the Reagan administration's stepped up military spending program.

While backing some new spending cuts, Treasury officials are, at present, opposed to increasing taxes, particularly after passage just three months ago of the $749 billion tax cut. They are less concerned with reducing the deficit than either Stockman or Domenici is.

The Regan-Stockman conflict is the second major deficit-reducing dispute the OMB director has engaged in since last August, when he lost out to Defense Secretary Caspar W. Weinberger in a fight to reduce defense spending.

In this case, House Republican leaders have lined up with Treasury Secretary Regan in the fight against tax increases.

While Domenici postponed committee action to next Tuesday, the Democratic-controlled House Budget Committee met but took no votes on the second budget resolution which will set revenue floors and spending ceilings. It is supposed to be passed before adjournment next month.

Just as on the Senate side, House committee members repeatedly complained that the White House has not set out in detail either its budget goals or its economic projections.