All the gray Washington day, Marshall Bradley and the men from Local 1110 swung their eight-pound sledges against the planks of the real Republican platforms, placing wooden boards on the green iron frames of bleachers in front of the White House. As many as 25,000 people will pay up to $100 to sit in those seats come Tuesday's inauguration.

Some people may be worried about getting a ticket for one of those prized seats, but Bradley was worried about splinters.

"You got to be careful," explained the burly Bradley, 21, lighting up a smoke on a recent freezing day along The Avenue of Presidents. "You bang them boards in wrong and somebody is gonna be a little uncomfortable, if you know what I mean."

And pigeons.

"You got to watch out for those flying boogers, too," Bradley said, though he had no advice other than "don't look up and wear a hat, I guess."

Bradley is one cog in the small army of hundreds of workers putting finishing touches on the reviewing stand, bleachers, platforms and other facilities that are specially constructed every four years to inaugurate a president.

But to Bradley and other construction workers, helping assemble the nuts and bolts of Ronald Reagan's inauguration is just another job. "I'll be here, in case anything goes wrong with the bleachers, but, well I didn't vote. I guess Reagan can't do no worse than Carter."

His coworker, 18-year-old Chris Kitts, from Charles City, Md., had a sarcastic view of what the inauguration will mean: "I bet D.C. will have a field day towing away cars," he said.

Nearby, General Service Administration carpenters were hammering doubletime to finish the reviewing stand -- from which the newly sworn president and his inner circle will watch the parade in heated comfort -- and the facing press stand, from which seasoned reporters will watch the president watch the parade, without the benefit of heat.

The cost of the bleachers, reviewing stand and press box, according to Laura Genero, of the Presidential Naugural Committee, is $1 million.

Elsewhere in the Capital City, the flurry is continuing and the expense tally is considerable.

On the West Front of the Capitol, 24,574 rented folding chairs are being positioned for Tuesday's swearing-in ceremony. Work is continuing there on the 20-foot-high platform where Reagan will take his oath of office. And while the "cosmetic painting" of the West Front of ther Capitol has been finished, workers are still installing restraining ropes and snow fences. The Joint Congressional Committee on Inauguration will end up spending about $440,000 on Tuesday's ceremony, according to the committee's officials.

The District government will spend at least the $1.3 million appropriated by Congress before the last remains of the parade confetti and horse droppings are finally swept away and the last overtime check written.

As a security precaution, manhole covers are being cemented down and trash cans removed from the parade route. Eighty spot-a-pots have been brought in, but some, explained D.C. Environmental Services Director William D. Johnson, are "gang toilets" with four or five seats. Including health inspections for the 200 street food venders expected major cleanings for all city streets and overtime, Environmental Services expects to spend about $126,000 on the event.

The D.C. Department of Transportation has budgeted $68,000 for the inauguration. $46,000 of which will pay workers' overtime. The remaining $22,000 will be spent erecting temporary no parking signs, closing off streets, removing some traffic signals from the parade route and the like.

The District, in cooperation with military authorities, will also be arranging all medical services. Even a horse ambulance will be provided.

About 150 local doctors and nurses have volunteered their time and services for the inaugural activities according to Mary Berkley, Chief of Emergency Health Services for the D.C. Department of Human Services. They will be supplemented with an equal number of military medical personnel, and additional numbers of emergency medical technicians from the fire department.

Back at the bleachers, Kitt, prodded by foreman John Kohansby, moved back toward his task. "I don't really understand why they go to all this trouble and spend all this money," he said.

"Pretty soon, everybody will start wishing Reagan had never been elected anyway," he said.