The budget-cutting mood that seized Congress this year did not quite extend to the massive public works bill yesterday, as the House approved, albeit by a slender margin, funds to continue building the $2 billion Tennessee-Tombigbee Waterway.

The immense waterway, the largest project ever undertaken by the Army Corps of Engineers, involves digging a canal to link the Tennessee and Tombigbees rivers to the Gulf of Mexico. In the process, engineers will move more dirt than was required to construct the Panama Canal.

Tenn-Tom's backers, a powerful block of southerners whose districts would benefit financialloy from the project, said it will encourage financially from the project, said it will encourage development and the export of Appalachian coal reserves. The project is more than half built, they added, and would cost more to dismantle than to complete.

Opponents, however, led by Reps. Joel Pritchard (R-Wash.) and Bob Edgar (D-Pa.), painted the canal as a classic example of pork-barrel politics in whcih incumbent congressmen use the federal public works budget to get re-elected. Tenn-Tom eventually will cost $3 billion, they argue, but the projected barge traffic, because of competition with the Mississippi River, will never materialize.

Pritchard's amendment, which lost 198 to 208, would have deleted $189 million targeted for the project in the fiscal 1982 energy and water appropriations bill, a massive piece of legislation that funds some 250 projects for $13.2 billion.

The House also defeated amendments to block funding of two other controversial projects: Stonewall Jackson Dam in West Virginia and Garrison Diversion in North Dakota. The challenges, even though unsuccessful, mark a significant change from only a few years ago when the public works bill was considered sacred and members rarely dared to vote against their colleagues' projects for fear of retribution.

While the Reagan administration supported Tenn-Tom, it had asked Congress to kill three other Corps projects that have been criticized as uneconomic and environmentally damaging: Louisiana's Red River Waterway, Kentucky's Yatesville Dam, and Big South Fork Recreation Area along the Kentucky-Tennessee border. The House bill, however, only deletes money for Big South Fork, while funding the other two.

Mississippi Democrat David R. Bowen said that if Congress abandons Tenn-Tom in mid-construction, when five dams have already been built, "you'd have the longest swamp in America. It would be an environmental disaster."

Rep. Jim Leach (R-Iowa), however, said "this is an issue of modesty -- whether Congress can recognize a past mistake. It's better to have half a white elephant than a whole one. We need a new direction on water projects, emphasizing a greater potable water supply for people, rather than new canals for industry."

A recent decision by the Fifth Circuit Court of Appeals suspended a major portion of the project until an environmental impact statement is prepared. The court said the Corps used an unlawfully low interest rate of 3.25 percent to calculate costs and benefits.

Opponents of the 232-mile canal also cited a General Accounting Office study this year that said the project would result in a barge traffic bottleneck at Demopolis, Miss., where the river narrows, and would thus require additional construction, at an extra cost of aobut $1 billion. Project supporters denied such improvements would be needed.

GAO and a Congressional Research Service report found that most coal shippers would prefer to use the wider Mississippi, or area railroads, rather than Tenn-Tom. Although shipment of Illinois coal is cited as a major benefit, Rep. Edward J. Derwinski (R-Ill.) said he discussed the matter with local operators and "it is far cheaper to move coal down the Mississippi."

Rep. Tom Bevill (D-Ala.), chairman of the subcommittee which has promoted Tenn-Tom for more than three decades, said however, "I've never seen such a phony attack on a project which has been studied more than any project in the world. "Bevill accused the railroads of funding the campaign against Tenn-Tom.

Among the local delegates, Michael D. Barnes (D-Md.) and Frank R. Wolf (R-Va.) voted for the Pritchard amendment while Steny Hoyer (D-Md.), Marjorie S. Holt (R-Md.) and Stanford E. (Stan) Parris (R-Va.) voted against it.