MONDAY NIGHT some 20 million Americans will see a CBS movie and learn what Washington has long known: Never bet against Mitch Snyder.

"Samaritan" is the story of Snyder's fight to get shelter for the homeless. Some of his less flashy fellow social-workers think he is more charlatan than samaritan, but Snyder's genius at public relations is such that he has, despite the most strenuous efforts of the Reagan administration to stop him, become "Mr. Homeless" in America.

Snyder, a onetime management consultant and felon (he was arrested as a passenger in a car rented with a stolen credit card and did time in Danbury), has been on the verge of extinction, literally and professionally, more times than a movie stunt man. He comes back smiling every time.

Snyder's methods are unconventional to say the least, and I am sure that in the public relations classes now taught in our universities, the professors would find his success exceptionally uninstructive. Snyder, when crossed, goes on hunger strikes and has vanquished a Navy secretary and a president. But fasting is, after all, not a weapon that yuppies wish in their dispatch cases.

Snyder might not have done so well with a less publicity-conscious group than the current tenants of 1600 Pennsylvania Ave. But the Reagan regime, ever conscious of television, could never quite face the prospect of seeing Snyder's funeral on the evening news. Snyder, they knew, would mock them from the grave.

The only person who stood up to Snyder was the Rev. James English of Holy Trinity Church. Mitch fasted in an effort to get him to allocate more money for the poor. Fr. English said that his parish was doing good works and declined to be blackmailed.

Others, however, were unnerved. Navy Secretary John Lehman, a combative, dug-in sort, capitulated and changed the name of a nuclear submarine from "Corpus Christi" (the body of Christ) to "City of Corpus Christi". Similarly, Ronald Reagan, on the last day of the 1984 campaign, gave in just as Snyder was about to give out and promised to make his grimy shelter at 2nd and D streets NW "a model."

When Reagan welshed, Snyder went to court. A federal judge made an extraordinary speech from the bench about Snyder's work and the pity of his clientele. But he ruled against him, and the government went ahead with plans to close the shelter and open a more structured establishment in Anacostia.

At this low point, Snyder had a stroke of the luck he shares with Reagan. Someone always comes along and rescues him from the pits.

In this case, the liberator was C. McClain Haddow, a high official of the Department of Health and Human Services. Haddow strapped on his helmet and sword and, apparently deterimined to win one for the Gipper, approached the court-ordered closing and eviction like the storming of an enemy fort. He bragged about "specially trained forces" under his command. It was the dead of winter and Reagan himself, from California, intervened to stop the invasion.

Snyder remarked somewhat smugly of the hapless Haddow, who has since left government: "He was willing to take me and the administration and 700 homeless people down in a hail of fire."

The administration then sponsored a competing shelter in Anacostia. Meantime, the White House began another and more elaborate plan to foil Snyder. In deepest, darkest secrecy, federal and district officials hatched a plot to convert six District schoolhouses into shelters at a cost, staggering in the era of Gramm-Rudman, of some $30-$40 million. Word got out -- it always does because Mitch Snyder has informers all through the government. It was noted in the press, with which Snyder is in constant touch, that Snyder takes no federal funds. With much gnashing of teeth, the White House canned its plan.

Snyder enjoys jousting with Ronald Reagan. They play on the same turf, with little regard for the rules and an eye ever to the camera. Snyder knows that homelessness is a subject of extreme irritation because it reminds people that it is not "morning in America" for everyone.

Hunger is another uncongenial topic, and the administration is also trying to kill the messenger. Dr. J. Larry Brown -- chairman of the Harvard School of Public Health's Physician Task Force, which produced a book called "Hunger in America" -- has been harrassed by a letter-writing campaign against his downbeat report.

Assistant Secretary of Agriculture John Bode wrote to Harvard President Derek Bok, complaining of "seriously flawed analysis" and "gross disregard for basic scientific method." The right-wing "Accuracy in Academia" chimed in with charges of "politically inspired propaganda."

Last week, Snyder attended a posh preview of his documentary. It was attended by movie stars and respectful officials and gave notice again to the most invincible politician of the age that, in a relentless agitator who gives and asks no quarter, Ronald Reagan has met his match.