If the Great River Road was a "farewell gift" to a retiring congressman, as some Capitol Hill humorists playfully claim, then it will go down as one of history's costlier remembrances.

The road is a scenic thoroughfare that, when built, will wind for more than 2,000 miles along the Mississippi River from source to mouth, through 10 states from Minnesota to Louisiana.

The price tag is already over $1 billion. Gasoline shortage or not, official stay-at-home urgings or not, the project has been easing right along since 1973, with about $110 million spent so far.

Nobody knows what the final cost will be. At last count, in 1977, when they stopped counting, auditors at the Federal Highway Administration estimated the Minnesota-to-Louisiana route would cost $1.2 billion.

But like many other public-works projects in this fiscal year's congressional appropriations package, the Great River Road is one of those ideas that Congress frequently decides has "can't fall" written all over it.

A number of administrations, including President Carter's, have not liked the costly idea, but its appeal in other precincts has been obvious and irresistible.

The 10 states like it so much that a Mississippi River Parkway Commission they formed in 1938 to promote it is still going strong. For every $1 the states spend on the road Washington sends them $3 more.

The 89 representatives and 20 senators from those 10 states -- that is, a fifth of the entire Congress -- are so numerous and well-placed that the project has had clear sailing since funding was authorized.

The idea of a parkway paralleling the Mississippi, a route that would channel motorists to the most scenic and historic spots, had kicked around for decades until it finally caught on in 1973.

The catching-on occurred under the direction of former Rep. John A. Blatnik (D-Minn.), who was chairman of the House Public Works Committee at the time. The route begins at Lake Itasca, the river's source, next to his old district.

Blatnik retired a year later, which gave rise to the jokes about a farewell gift, but once spending was authorized, the Great River Road was on the way to reality.

With Blatnik's departure, the Great River Road's chief defender became Sen. John C. Culver (D-Iowa). As a House member he helped Blatnik promote the authorizing bill. As a senator after 1974, he fended off occasional attacks on the project's cost and scope.

When it is completed, the Great River Road is to consist of stretches of new highway and upgraded old highway mostly all two-laned, paralleling and crisscrossing Old Man River.

Back and forth, over existing bridges, the road is to run from upper Minnesota to the Gulf of Mexico, taking a traveler past historic and scenic wonders in parts of each of the 10 states.

The scenery and the historic sites have been there awhile, but as Vincent Cileti, a programs official at the Federal Highway Administration, noted, the 10 states did not get enthusiastic about promoting them until the lure of federal development dollars showed up.

The Parkway Commission keeps close tabs on each state's spending, and spurs them to continue coming up with the money that will assure a flow of the 3-for-1 matching cash from Washington. The federal money is from general tax revenues and the Highway Trust Fund.

The Great River Road idea surfaced during the Roosevelt era of the 1930s, but one administration after another since then resisted putting up the money for it.

"A decision was made a long time ago," Cileti said, "that it was too vast a venture for the federal government to fund . . . It was thought to be better to let each state proceed on its own if it wanted to develop a scenic river road."

But finally Congress couldn't be deterred.