Once hailed as a model in the control of water pollution, a half-finished maze of subterranean sewers here known as "Deep Tunnel" has become an engineering extravaganza so ambitious that it may never be finished.

The tunnel and reservoir project (TARP), as it is officially known, was originally expected to cost about $1 billion, but the latest government estimate puts the total at $12.5 billion, or more than it cost to build the trans-Alaskan pipeline.

If TARP is completed, there will be 131 miles of concrete tunnels, pump stations, drop shafts and reservoirs far below the streets of Chicago, enough to store and treat 44 billion gallons of water.

The tunnel is the ultimate water project: a scheme to prevent flooding in Chicago, which was built on a swamp, by storing excess rainwater underground until it can be drained away slowly after the danger of flooding is past.

TARP was planned in the era of big federal public works grants and designed to solve a problem that plagues dozens of older cities: combined sewers, sewers that carry rainwater and residential and industrial sewage through the same system. When it rains, they invariably overflow, causing widespread flood damage.

That happens here on the average of once every four days, spewing tons of raw sewage into basements and into the Chicago River, a filthy industrial waterway that slices through the business district.

Sewers used to be a local headache. But since the federal Clean Water Act was passed in 1972, the Environmental Protection Agency has churned out billions of dollars for local sewage-treatment plants and advanced pollution-control equipment. As states and cities lined up to build increasingly expensive projects, this rapidly mushroomed into another budget-busting program.

But the Reagan administration, after cutting the water pollution control grants from $4.2 billion to $2.4 billion, is now pushing for even deeper cuts. EPA is about to issue proposed rules that would allow local officials to lower their water quality standards. And Congress has singled out combined sewer projects as a particularly low priority.

The Reagan policy means that many urban areas may have to find a less expensive solution for combined sewer backups or forget about the problem. Nearly a third of Washington's sewer system, for example, carries both rainwater and sewage, which often overflows into the Potomac and Anacostia Rivers.

No one is sure whether to keep pouring money into Chicago's half-finished tunnel. EPA has picked up 75 percent of the tab, but the agency is still trying to decide whether to finish paying for it.

TARP is the brainchild of the Metropolitan Sanitary District (MSD), an agency that helps provide water and sewer service to more than 4 million people here. In classic Chicago style, the city's Democratic machine helps elect most of the nine sewer commissioners, and they, in turn, issue contracts to companies that sometimes contribute to Democratic candidates.

"We have been less than honest--even deceptive -- in presenting this to the taxpayers of Cook County Chicago as a solution to their flooding and pollution problems," said Joanne Alter, the only sanitary district commissioner who opposes the project.

"In truth, my fellow commissioners knew we weren't going to finish it because there weren't funds available, but they still went out and campaigned for this as the greatest thing since white bread."

Hugh McMillan, the sanitary district's superintendent, strongly disagrees. "Every day after a rainstorm, you walk down Michigan Avenue to the mouth of the Chicago River and you see the filth floating in the river," he said. "We've also got a hell of a flooding problem affecting 1 1/2 million people. When you look at it in that context, the cost of TARP is an absolute pittance."

MSD officials often point to the federal goal that all waterways should be "fishable and swimmable" by 1983. But that standard only has to be met "wherever attainable," and no one expects to be catching fish in the dirtiest parts of the Chicago River. Illinois has a much lower standard known as "secondary contact," which means that if you took an accidental dip in the river, you would probably survive.

The sanitary district has a long history of thinking big: in 1899, it managed to ship its pollution downstream by reversing the flow of the Chicago River. So, in the early 1970s, the agency brushed aside suggestions for less expensive solutions and designed TARP as a huge storage tank that could "bottle" a rainstorm until the sewage overflow was treated.

"Everyone here is very cautious about coming out against TARP," said Donald Hey, an engineer who served on a task force that criticized the project. "The MSD lets a lot of contracts, and engineers here are very interested in working for them."

In fact, the engineering contracts were awarded without competitive bidding, and when some of the bids came in well above the estimated costs, the sanitary district raised the estimates. This enabled MSD to claim later that there were no cost overruns.

A grateful construction industry helps finance many of the sanitary district campaigns. Nicholas Melas, the sanitary district president, has received more than $28,000 in contributions from trade unions and contractors, several of whom have received substantial awards to help build TARP.

For example, Paschen Contractors, which has given $3,000 to Melas and $2,500 to Mayor Jane Byrne, also happens to be part of a joint venture with a $107 million contract to build a 4.8-mile segment of the tunnel.

"Historically, there have always been very close ties between the major construction firms and the Chicago political organization," said Alter, a dissident Democrat.

"Joanne is part of the white-wine-and-cheese set, leading the charge for whatever's fashionable," responded Commissioner Richard Troy, a TARP supporter.

Company President Bill Paschen views it this way: "We agree with TARP and therefore we would back the candidates who support TARP. It's part of the political process."

In the five-mile segment that Paschen began in 1977, the tunnel is four stories tall, 35 feet wide and lined with 12 inches of concrete. The musty, cylindrical tunnel resembles an empty Metro station, complete with railroad cars and tracks to move equipment across the muddy floor.

An 800-ton hydraulic boring machine, known as a "mole," has smashed through the rock behind a large set of steel blades. Drop shafts have been drilled to carry the rain 30 stories below ground.

All this digging has left millions of tons of excavated rock towering like small mountains above each construction site. This produced a small uproar when the sanitary district gave away about $100 million in limestone to two local contractors, who proceeded to sell it to the highest bidder.

The furor began in earnest in 1978 when Sen. Charles H. Percy (R-Ill.), a frequent TARP critic, asked Congress' General Accounting Office to review the project.

The auditors now say the sanitary district grossly understated the expense by leaving out such related costs as $1.1 billion for a new sewage treatment plant and improvements at two other plants, $2.6 billion in interest during construction, $353 million to widen and dredge the Chicago ship canal, $56 million a year in maintenance costs and $32 million to improve water quality by pumping in 165,000 pounds of oxygen a day.

In addition, they said TARP would have little impact unless suburban communities spend $2.2 billion to upgrade and expand their local sewers. "We would have to raise property taxes or water rates," said Mark Schoeffmann, the village engineer in suburban Skokie, which would need to spend about $100 million. "It's a very big issue in most of the towns."

McMillan gets angry at any mention of the congressional auditing agency. "Some of these numbers are absolutely fictitious," he said. "The GAO report was done to produce a horror story about this type of project. GAO took every water management project in the metropolitan area and dumped it into a bag and called it TARP."

McMillan also scoffed at GAO's suggestion that disconnecting downspouts on buildings, collecting rainwater on rooftops and other alternative measures could ease the flooding problem. "They don't work," he said.

McMillan's office is filled with maps, charts and slides to demonstrate the benefits of TARP's Phase I, which he says will reduce sewer overflows from 100 to 10 a year and capture most of the pollutants now entering the river.

He is equally enthusiastic about Phase II as a means of eliminating nearly all sewer overflows, reducing more than half the flood damage and stopping sewer backflows into Lake Michigan. These backflows have caused beaches to be closed on several occasions.

But few people see any light at the end of this tunnel. EPA won't pay for Phase II because it deals with flood control, and the Army Corps of Engineers, which is studying the issue, would need permission from Congress to get involved.

Nor is it likely that local residents could pick up the tab: the sanitary district has more than tripled local sewer taxes over the last decade while its bonded indebtedness has increased more than sixfold to $650 million.

"The MSD has been grinding up taxpayers' dollars with grandiose schemes for years," said Gary Rowe, an aide to Percy. "Mayor Richard Daley once said he looked forward to the day he could swim in the Chicago River and pull salmon out of it. Well, that day will never come. It's a wild pipe dream."