President Carter said flatly yesterday that he will veto the public works spending bill now awaiting action in Congress if it exceeds his original budget recommendations or includes unwanted water projects. The House is scheduled to begin voting on the bill today.

In a nationally televised press conference in which he intensified the pressure to fight inflation by restraining spending, Carter said he was "concerned in particular" about the public works bill because it would add $1.4 billion in spending for more than 40 new water projects and continue outlays for several others that Congress had agreed to defer.

Carter said the administration would be working in the next few days "to eliminate the unnecessary spending proposals for water projects" now in the bill. "Unless they are all eliminated," he added, "I intend to veto" the legislation.

Meanwhile, administration sources disclosed the White House has completed a list of 37 bills that officials have targeted for possible veto by the president - including eight appropriations and authorization bills regarded as major pieces of legislation.

Presidential spokesmen, including James T. McIntyre, the director of management and budget, reportedly delivered the president's warnings about possible vetoes to the House leadership on Tuesday. There was no indication whether the leaders agreed to support the president.

The developments came as Congress, in a series of votes yesterday, provided a crazy-quilt response to Carter's budget warnings, voting to make further cuts in spending bills on one hand and reversing some earlier reductions on the other.

In floor action yesterday, the House first deferred on a point of order about half of an $8.6 billion appropriations bill for the departments of State, Justice and Commerce - taking congressional budget process alowing such actions.

Later, it refused 203 to 200, to drop from the $30 million earmarked for the Legal Services Corp. But then advantage of a loophole in the new it agreed to slash the bill 2 percent, or about $90 million, across the board. The House then passed the measure.

The 2 percent cut came despite warnings by House Speaker Thomas P. (Tip) O'Neill Jr. (D.Mass) that if the lawmakers began cutting back on key Democratic "bread-and-butter"programs they would then run the risk of building momentum for slashing other proposals across the board.

And, separately, a Senate Appropriations subcommittee voted to reverse Tuesday's House action trimming 2 percent from the Labor-HEW money bill. The subcommittee first voted to overturn the House action, then to add several billion dollars in new spending.

The subcommittee's action would bringthe cost of the legislation to about $500 million over what the House had voted Tuesday and what the administration had budgeted. Revised estimates showed the House actually trimmed only $385 million, not the $800 million reported earlier.

Meanwhile, Barry P. Bosworth, director of the administration's Council on Wage and Price Stability , warned that the nation may be headed for a recession if the government does not show some progress against inflation in the next six months.

Bosworth originally told a meeting of the Air Line Pilots Association that he gave the economy "no more than six months . . . if we don't do something this year, we are going to go back into a recession." However, a council spokesman later softened those remarks.

The major fight over the $10.3 billion public works bill is expected to come today, on a White House-backed amendment by Rep. George Miller (D-Calif.) that would strike 28 of 41 water project proposed in the measure and substitute 11 new projects Carter endorsed last week. The administration had not targeted these new projects as objectionable until Tuesday.

The White House position has strong support from environmentalists, who oppose many of the water projects as detrimental to fish and widlife. However, elimination of any of the projects is expected to be fought vigorously by members of the Public Works Committee.

Five of the water projects the administration wants cut are in Texas, the home state of House Majority Leader Jim Wright.Rep. Tom Bevell (D-Ala.), chairman of the House Public Works appropriations subcommittee, insisted yesterday the projects "are not inflationary."

In other action yesterday, the House also voted 241 to 158 to prohibit the use of funds in the State, Justice and Commerce bill for promoting trade with Cuba. The provision is expected to have no practical effect, but was interpreted as a sign of House disapproval of Cuban actions.

Along with the public works appropriations bill, the list of possible "veto targets" the administration has compiled includes the defense authorization bill, the Labor-HEW spending bill, the Department of Transportation authorization bill, and agriculture bill.

In the defense bill, Carter is said to object to about $4 billion in authorization levels that exceed his own budget requests - including $2 billion in authority to begin a new nuclear powered aircraft carrier and $1 billion for a neclear strike cruiser.

Officials said the transportation bill contains $16 billion more than Carter wants. Moreover, while the measure would authorize about $60 billion worth of spending for the six-year period, it actually would allow the government to spend the money in four years.

Carter also is eyeing critically the Public Works authorization bill and measures to provide funds for veterans' pensions and impact aid to education. Presidents have been trying to get rid of the impact aid program for years - always without success.

Apart from these major bills, White House officials also have prepared a list of dozens of less-important measures the administration considers inflationary, including measures affecting Indian claims, a moratorium on grazing fees, nursing amendments and a bill reducing the work week for federal firefighters.

McIntyre is said to have told congressional leaders Tuesday that the battle over the budget is "the most significant thing" the administration has "pending before Congress today." The OMB director has been among those pushing for a tighter budget.

Officials also disclosed yesterday that Carter now hopes to push the budget deficit for fiscal 1979 - the spending plan he submitted last January - to below $50 billion, rather than the $55-billion-to-$56-billion level that budgetmakers now expect.

The administration also has altered its projections for the current year's budget deficit, to $50 billion, down from the $53 billion now on the books. Officials say the $3 billion "cut" will come mainly because spending is falling short of official expectations.

The series of White House and congressional actions came in the face of mounting pressure on federal government following last week's approval in California of Proposition 13 - the measure the ordered a cut in local property taxes there.

Carter said in his press conference yesterday there was "no doubt" that unemployment will rise in California as a result of last week's voting. He said many of 50,000 public service jobs now supported in the state through federal financing "may be in danger."

At the same time, however, the president confirmed suggestions by other officials earlier that the federal government would not move in to help California if the tax rollback gets the state into trouble financially.

"We have no inclination to single out California over other states just because it has cut property taxes," Carter said.