The day after President Reagan proposed cutting the domestic budget by $40 billion, Republican Sen. Orrin G. Hatch of Utah sent out two press releases.

The first one, which praised the deep reductions in spending, was headlined "Hatch Pleased with Budget Cuts." The second one, aimed more at the voters back home, declared: "Budget Cuts Won't Slow Down Completion of Central Utah Project, Hatch Says."

The senator was reassuring his constituents last February that while he would help take the ax to major portions of the budget, he would continue to protect a controversial $1.5 billion project to pump vast amounts of water 156 miles from the Colorado River to Salt Lake City.

This massive federal undertaking--which includes 10 new reservoirs, three power plants and 140 miles of aqueducts, canals and tunnels--would seem to typify the kind of big government that Hatch has made a career of denouncing.

During the intense political struggle over the budget last year, Reagan and his allies in Congress argued long and vigorously for the need to cut federal spending. Nowhere were the battle lines more clearly drawn than in the Republican-controlled Senate, where many of the president's supporters embraced the sweeping cutbacks in health care, education and welfare aid for the poor.

Throughout this painful budget-cutting process, however, more than 300 water projects emerged almost unscathed, including several that Reagan had targeted for extinction.

These include dozens of "pork barrel" projects that graphically demonstrate the legislative clout of each senator. They range from such huge undertakings as Hatch's Central Utah Project to a small dam to control flooding at Willow Creek in Oregon, which was inserted in the budget by Senate Appropriations Committee Chairman Mark O. Hatfield (R-Ore.).

"I have to confess to you, that's just raw political power," Hatfield said of the dam. "I make no apology for that. I just put a value on human life. They'd petition to have me hanged at high noon if I didn't do anything about Willow Creek."

The cost of all these water projects is considerable, even by congressional standards. The Army Corps of Engineers now is building 284 such projects that will cost an estimated $26 billion, while the Interior Department's Bureau of Reclamation is working on 69 projects worth another $14 billion. Both agencies are studying even more water projects that could cost an additional $34 billion.

Some of these projects are vital to development in the parched western states, although there is considerable debate about their size, cost and environmental impact.

Others, especially some dams, parks and irrigation canals, are widely regarded as marginal, providing what opponents describe as just another federal subsidy for local farmers and developers. Still, many of the projects in both categories have been protected with equal fervor by senators who generally direct their legislative energies toward cutting the budget.

"These people are only selective fiscal conservatives," said Brent Blackwelder of the Environmental Policy Center. "Not a single water project was touched by Congress this year."

Blackwelder and other environmental activists say the Central Utah Project, for example, will damage 200 miles of scenic trout streams, destroy 28,000 acres of wildlife habitat and take substantial amounts of water from the Ute Indians with only vague promises of future compensation.

Former President Carter put the Central Utah Project at the top of his "hit list" of wasteful water projects in 1977. But Hatch, the earnest, outspoken chairman of the Labor and Human Resources Committee, twisted enough arms on the Senate floor to rescue it.

"We have continued to make sure this project is funded because it's crucial to the state," Hatch said in an interview. "To cut that budget would be foolish and not cost conscious. It's difficult for people here to understand that in the West, and in the second dryest state in the union, water is a matter of life and death for us."

Hatch blamed delays by the federal government for the fact that the project's cost has mushroomed to more than four times the original estimate of $365 million. But he said this is not a government subsidy because Utah will use much of the water to develop oil, gas and mineral reserves that will benefit the entire country.

"If this was a brand new project being proposed today, I don't think it would fly because of the budget situation," Hatch said. He said local residents eventually would repay a substantial part of the cost through water charges, but that it would be unfair to make them share the cost now "because the federal government has always promised to advance the funds."

Senate staffers, however, say the Central Utah plan, like many others, calls for water users to repay only part of the cost at low interest rates over a 50-year period, which amounts to a generous gift to local residents from the federal treasury.

Hatch's colleague, Sen. Jake Garn (R-Utah), has supported the project since he was a water commissioner in Salt Lake City. "To make larger cuts would be totally counterproductive," said Curt Burnett, Garn's press spokesman. He said Garn believes that any local cost-sharing plan "would have to be phased in over a period of years so it won't be an unbearable burden."

Congress also has approved a long list of dams and parks that are close to the hearts of key senators, but which opponents consider questionable at best. Some legislators argue that the Army Corps of Engineers helps to promote these projects by devising unrealistic "cost-benefit ratios" that rely on such outdated assumptions as borrowing money at a 3 1/4 percent interest rate.

The Columbia Dam in Tennessee, for example, is supposed to provide recreation and increase the water supply in Howard Baker's home state. But the National Wildlife Federation says the $153 million dam would wipe out 440 farms, eliminate 54 miles of the scenic Duck River, destroy fish and wildlife habitats and force the relocation of 1,500 people.

"We've built 50 major reservoirs in the Tennessee Valley, and this represents the bottom of the barrel--the dregs," said Edward Osann of the wildlife federation.

Still, these calculations leave Baker out of the equation. While assuming the duties of majority leader last year, Baker has remained devoted to the care and feeding of the local Tennessee interests that demand these projects. The current Senate budget, therefore, directs the Army Corps to speed up work on the Columbia Dam.

Tom Griscom, Baker's press spokesman, said the senator supports the Columbia Dam but has merely followed the advice of the Tennessee Valley Authority on the project. Even the TVA, however, has acknowledged that the project's costs outweigh its benefits.

Baker has played a more active role in securing funding for Big South Fork Park, a scenic riverside wilderness along the Tennessee-Kentucky border, Griscom said. The Reagan administration tried to terminate the $103 million project, but Baker, while agreeing to eliminate some scenic trails and recreation areas, managed to push through $9 million this year to keep construction of the park on schedule.

A glance at the Army Corps of Engineers budget for 1982 might leave the impression that most of the nation's water flows through Oregon. It may be more than a coincidence that the state's senior senator chairs not only the Appropriations Committee, but its subcommittee on energy and water development.

"The number one porker around here is Mark Hatfield," said one Senate aide.

There is more than $170 million in the federal energy and water budget to study, build, operate and maintain more than 50 water projects in Oregon, compared to just 13 in Idaho and 12 in South Dakota.

One of the most costly and controversial items is the Willow Creek dam that Hatfield pushed through the Senate for the town of Heppner, Ore., population 1,500.

The town had a disastrous flood in 1903 that killed several dozen people, and has suffered occasional flooding since. Environmentalists say the $45 million dam is in the wrong place to control the flooding, and even the Army Corps of Engineers--which often is accused of excessive optimism in such matters--says the cost of Willow Creek far outweighs the potential benefits.

Marshall Lovegren, Heppner's town administrator, said many local farmers oppose the dam because they would lose their land. "Forty-five million dollars?" he said with a laugh. "Hell, that's more than the town's worth."

Hatfield also added $3.4 million to design a new Bonneville Lock, the first and smallest lock along Oregon's well-travelled Columbia River. Hatfield says the lock, which raises and lowers the water level so barges can get through, is becoming a bottleneck to commercial traffic.

"The Bonneville Lock is one of the highest priorities I have," Hatfield said. Army officials initially balked at the expensive project, which environmentalists say would serve mainly barges carrying inexpensive sand and gravel.

The Republican senator also found $1.3 million to design a dam for Elk Creek in southern Oregon.

But Rep. James Weaver (D-Ore.), who represents the area, said the $108 million dam is "an unnecessary, uneconomical and ill-advised pork barrel project." Weaver says the flood control benefits are nonexistent, the recreation benefits "vastly overstated" and the water quality improvements "a sham." Hatfield said he has agreed to move slowly on the project until further studies are completed.

Hatfield points out that he has trimmed about $200 million from the total budget for water projects.

Still, much of the committee's budget report is filled with instructions to the Army Corps in Oregon: to speed up work on a Columbia River powerhouse, to improve hazardous conditions on the Chetco River, to launch a $450,000 study of whether the port of Astoria can be deepened to accommodate coal shipments. There is also money for an Oregon fish hatchery to help replenish the salmon that environmentalists say have been driven away by the dams.

"That's the way the system works," Hatfield said. "I can't help it that I'm chairman of the Appropriations Committee."

One of his freshman colleagues on the committee, Sen. Mark Andrews (R-N.D.), has been pushing a massive irrigation project for his home state. The billion-dollar Garrison Diversion Project would carry water across North Dakota to irrigate 250,000 acres of prime farmland, but it would take nearly as much fertile soil and wetlands out of production.

The National Taxpayers Union says this irrigation would benefit fewer than 1,000 farms, amounting to a federal subsidy of more than $800,000 for each farm.

"That is just sheer, unadulaterated pork," said Sen. William Proxmire (D-Wis.). "But Andrews went around telling people, 'It's in my state and we need it.' "

Ed Doherty, a spokesman for Andrews, said the senator believes there would be no environmental damage and that the project would encourage industrial development while providing water for 22 cities. "We look at these things as an investment that will bring in money," he said.

Construction of the Garrison project has been halted by an environmental lawsuit, but Andrews pushed an amendment through the Senate directing the Bureau of Reclamation to ignore the court order and spend $4 million on the project anyway. The House has refused to go along.

Others are still trying to get their water projects off the drawing board. Sen. James Abdnor (R-S.D.), another 1980 freshman on the Appropriations Committee, has been pushing without success for a $500 million hydroelectric plant for South Dakota. He feels his state deserves the project because it never received the promised benefits after the Army Corps built a series of reservoirs in South Dakota that claimed 500,000 acres of prime farmland.

"We didn't ask for those reservoirs," Abdnor said. "We have nothing to show for it but a little fishing and boating."

The Democrats on the committee, meanwhile, have hardly remained idle. Minority Leader Robert C. Byrd (D-W.Va.), for example, managed to secure $17 million this year toward a new dam at Stonewall Jackson Lake, which includes a special million-dollar swimming lagoon.

As the ranking Democrat on the Appropriations subcommittee on the Interior, Byrd also knows how smaller projects can be hidden in the committee report. This year's report language happens to include $2 million to acquire parkland at New River Gorge, $255,000 for a fish hatchery at White Sulphur Springs and $85,000 to pay police to handle the tourists at Harpers Ferry.

There are also several major water projects for Louisiana, a legacy of the days when Sen. J. Bennett Johnston (D-La.) headed the energy and water subcommittee. The largest one, a combined water and transportation project, is the $1.7 billion Red River Waterway, which would carry commercial barge traffic from the Mississippi River to Johnston's home town of Shreveport.

Early last year, Budget Director David A. Stockman tried to kill this inland waterway. But Johnston and Sen. Russell Long (D-La.) paid a visit to Reagan, talked to most of their colleagues, and came up with $50 million this year for the 150-mile waterway.

While Reagan publicly continued to oppose the project, Senate aides said the White House didn't lobby very hard against it.

"Our position is that the whole nation benefits from any kind of transportation system," said Johnston aide Skip Walton, who says the waterway will enable barges to carry agricultural products from the fertile Red River Valley. "We didn't see why this one project should be singled out."

But Osann of the National Wildlife Foundation said the project is more important to Louisiana politicians than to Southern producers and shippers. "It would claim thousands of acres of farmland and woodland, and you would spend $2 billion to get to Shreveport when there are railroads and highways that go there right now," he said. "It's a classic redundant, politically contrived project."