THOSE 16 BLOCKS of Aquia Creek sandstone that fell from the Capitol's west facade nine days ago may turn out to be the pieces that broke the decades-old deadlock over whether to extend the West Front or to restore it.

Pictures of the dark blotch of rubble-and-brick foundation left exposed by the fallen stones were printed and televised across the country. Legislators began to wonder with a new sense of urgency what constituents would think of a group that allowed such blemishes to appear on the nation's most famous political landmark.

Whether this augurs well or ill for the great building remains to be seen. But Rep. John F. Seiberling (D-Ohio), an award-winning preservationist who, ironically, favors extension of the building, expresses a widespread feeling when he says, "I'd say that this time something will be done. I don't know how it's going to come out, but something will be done."

Things are moving rapidly toward a showdown. Next week the House Appropriations Committee is expected to report favorably on the $73 million extension plan. A vote on the House floor could come before the month is out.

If history repeats itself, the House would narrowly approve extension and the matter would die in conference with the Senate, which, under the leadership of Sen. Ernest F. Hollings (D-S.C.) and, more recently, of Sen. Alfonse D'Amato (R-N.Y.), has consistently favored restoration. The last recorded House vote was 212-204 for extension. This was in 1977 when Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) "was down in the well twisting arms," recalls Rep. Samuel S. Stratton (D-N.Y.), who was on the opposite side of the issue.

O'Neill recently said he thought he could push extension through the House "without too much difficulty, having talked with some of the fellows." But lobbyists for restoration are guardedly optimistic about a different outcome. Stanley Kolbe of the American Institute of Architects points out that of the House members still present from that vote, 125 were for restoration and 95 were for extension. "The preservation ethic is stronger among the new members," he says, "and besides, they don't see anything in it extension for them."

Michael Ainslie, president of the National Trust for Historic Preservation, said his group has mailed alerts to 12,000 preservation "activists". Next week the National Trust will have Mailgrams supporting restoration delivered to its 130,000 members. The group's main push, Ainslie said, will be a rally on the West Front steps at noon Thursday.

Each House speaker from Sam Rayburn of Texas (who pushed through the expansion of the East Front in the 1950s) to O'Neill has aggressively pursued extension. One reason, in Stratton's view, is: "They figure they want to sort of leave their mark on the Capitol. After all, Rayburn got his side done."

The reason cited more frequently is space. House leaders say that senators got more than they did from the East Front expansion, and they point to overcrowded House committee rooms in the Capitol. But precisely what else would go into the new addition has not been spelled out in detail. Seiberling mentions the need for a "really good library" and reception rooms for visitors, and O'Neill, at a recent meeting of the Commission on the West Central Front of the United States Capitol, said, "You could put a really first-class dining room in."

Like his predecessor George Stewart, Achitect of the Capitol George White has been a leading advocate of extension. "A lot of people wanted to know where George White was when those stones came out," joked an experienced observer of the long-stalemated debate. White, who was appointed by President Nixon in 1971, took advantage of the event at a press conference the next day to publicize his extension plan.

White's proposal is not so large as Stewart's--his would provide about 80,000 usable square feet, about half as much--and it would not physically alter Frederick Law Olmsted's beautiful west steps and terraces. Stewart's plan would have ruined these. Still, the newer plan would dramatically change the look of the building by partially filling in the sunken courts between the central portion and the Senate and House wings, and would significantly alter the relationship between the the Olmsted terraces and the building. As currently set, these terraces make a spacious pedestal for the building. Extending the central facade 22 feet as planned would squeeze the space.

Both sides look to history for justification. White and other supporters of extension maintain they would simply be completing the structure as intended by Thomas U. Walter, the Architect of the Capitol who designed the magnificent cast iron dome and the big new wings in the 1850s and 1860s. "It is an unfinished building and I expect to finish it, under the same regimen that I executed the portions of the building already completed," Walter wrote.

Opponents of extension can match White quote for quote. In 1904 a Joint Committee of the Senate and House for the Extension and Completion of the United States Capitol reported, vis-a -vis Walter's plan: "When we read this report accompanying his plans of 1865 we were impressed with the feeling that Mr. Walter had been influenced, perhaps under pressure from Congress, by the desire to obtain increased accommodations within the building, and that he would have recommended a somewhat different treatment if he had had under consideration only the strictly architectural necessities of the design."

That committee recommended that "it would be better to reproduce the present design in marble, as nearly as possible as it now stands . . ." Today preservationists reject the idea of a marble sheathing for the old sandstone wall almost as vociferously as they attack the notion--archeologically correct, but strange--that by hiding the old wall behind a new addition we would be preserving it for posterity. Ainslie says, "The appearance of the sole remaining original wall of the United States Capitol is of great emotional significance to people."

White has argued repeatedly that the small difference in costs--$66 million for restoration versus $73 million for extension--justifies the latter course. "We'd get the added space almost for nothing," he says. But the figures are questionable. In arriving at them the office of the Architect of the Capitol used a 35 percent contingency allowance for unforeseen problems in the restoration and only 10 percent for new construction. Using a more customary 15 percent contingency allowance for restoration brings its cost down by about $10 million.

Furthermore, as pointed out by Edward Cohen, managing partner of Ammann and Whitney, the New York consulting firm that prepared detailed studies for restoration, the proposal includes about $7 million worth of work on the terraces, which unlike the west wall are not in dire need of structural repair. Congress should perhaps take this opportunity to do work on the 90-year-old terraces, but it does seem fair at the beginning to separate these costs from restoration of the central west wall.

The course is hard to predict. There are four possbilities. If restoration wins on the House floor, the debate would be over, for the Senate obviously would go along with that. If O'Neill coaxes out another floor victory in the House for extension, the matter will be taken up in conference with the Senate. This could go three ways: restoration, extension or continued stalemate.

O'Neill, the old pro of the Hill, has stacked the deck as heavily as possible in his favor. By attaching the issue to a grab-bag appropriations measure (the fiscal year 1983 supplemental appropriations bill), he has assured himself a parliamentary edge on the House floor and, should he win, a large, complicated conference session. As one veteran Senate-side observer of the stalemate points out, "It's impossible to say what will happen at 4 o'clock in the morning at one of those conference sessions . There are a lot of issues, a lot of urgent items. Somebody could say, 'Oh, let them build it.' "

Elliott Carroll, executive assistant to the Architect of the Capitol, mused the other day, "If Congress had decided to use marble in the first place, maybe we wouldn't be arguing this today." As an economy move in the 1790s, Congress choose sandstone from the Aquia Creek quarry in Virginia over marble from nearby Cockeysville, Md., because the sandstone could be brought by barge up the Tiber Creek to within 200 yards of the construction site.

As the Ammann and Whitney report noted, these blocks of stone come from "a Lower Cretaceous (that is, 60- to 80-million-year-old) sedimentary stratum composed of quartz sand, pebbles and clay pellets, cemented by silica. The cementation is weak and the stone is of poor quality as a building material." Protected only by paint--some 30 layers reflecting "a history of the American painting industry"--these stones have lasted nearly two centuries.