A businessmen`s outfit called the Coin Coalition is lobbying hard this congressional session to have the federal government abolish the venerable penny, rendering obsolete such phrases as ''a penny for your thoughts'' and

''a penny saved is a penny earned''--the latter believed to have last been uttered in Congress in 1832.

The coalition complains that American business is losing millions in sales and manhours because checkout lines are being held up by customers scrounging for pennies or clerks looking for change. ''What can you buy for a penny today?'' said a spokesman for the group, which is represented by the same lobbying firm that pushed through the extension of Daylight Saving Time last year.

As an alternative, the group is proposing that all prices be rounded off to the nearest nickel. This would net retailers a nifty extra profit of as much as four cents on every item, of course, but then, they could no longer sell things at bargain prices of $99.99.

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The Treasury Department has other problems--such as six-foot green monsters showing up at news conferences.

One of the first things James Baker did upon giving up running the country as White House chief of staff and taking over running the economy as treasury secretary was to kick the Treasury Department press corps out of its comfy, off-by-itself press room into much less comfy and much more public quarters opposite the main visitors entrance. At the same time, he made longtime aide Margaret Tutwiler, a high-born Alabama lady, his assistant secretary for public affairs.

Tutwiler is famous in Washington Redskin circles. Trying to secure top-dollar seats for Baker and friend one day, she found herself talking to quarterback Joe Theismann. Comprehending finally that his job did not include issuing tickets, she dismissed him with, ''Why am I talking to yew?''

Though she serves as the department`s chief press spokesperson, Tutwiler has never once appeared in the new press room, which is one of the reasons it has been named the ''Margaret Tutwiler Memorial Press Room.'' Not content with that, the Treasury newsies acquired a six-foot inflated Godzilla of Japanese monster movie fame, issued it its own official Treasury Department credential and gave it a prominent place in the press room for all passing visitors to see.

Still not content, the newsies took Godzilla to a high-level Treasury news conference this month. No, the officiating official did not ask it a question. The official had been ''briefed'' that Godzilla was coming, and studiously ignored its presence. Yes, Godzilla is also known as ''Tut the Magic Dragon.''

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Rep. Morris Udall (D., Ariz.) is planning to introduce legislation to establish a new $1 coin. Unlike Jimmy Carter`s ill-fated Susan B. Anthony dollar disc, which resembled a quarter and made Real Men feel embarrassingly like feminists when they plunked it down at Mongo`s Bar and Grill, the Udall dollar would be man-sized. It also would contain a lot of copper, as does his beloved Arizona (A copper dollar minted is a dollar earned for the Arizona copper mines?).

This would not solve the problem of what to do with the $500 million in Susan B. Anthonys the Treasury still has stored away for a very rainy day--a problem that now ranks in insolubility with the what-to-do-with-nuclear-waste problem. It would also further undermine the saying, ''What this country needs is a good five-cent cigar.''

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Former Vice President Walter Mondale has finally won fame, at least the same kind of fame won earlier by such fellow former veeps as the immortal Daniel D. Tompkins, Richard M. Johnson and Thomas A. Hendricks. A bust of Mondale is to be produced by sculptor Judson Nelson, whose previous commissions have included a work in Grand Rapids` Gerald R. Ford Museum, and placed in a Senate hallway. It`s said that the marble bust will vividly evoke Mondale`s spell-binding performance on the campaign trail in 1984.

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Last week, patrons of one of Washington`s most popular pizza parlors were stunned to learn that the owner is being investigated by the feds, who suspect him to be a Mafia enforcer nicknamed ''the butcher.'' This week, patrons of the capital`s most popular soul food eatery were shocked to learn that it has been fingered as a major fence operation with jade horse statues and gold jewelry reportedly being traded at the cash register during lunch hour. Not long ago, it was learned that ownership of one of Washington`s sin strip girlie saloons had been taken over by the FBI.

And down at McDonald`s, there`s this clown. . .