IN HIS STATE of the Union address this evening, President Reagan is expected to kick off his campaign to persuade Congress and the public to buy his budget proposals. It won't be an easy sale. As Republican Sen. Mark Andrews remarked the other day, the budget promises "enough horror to scare the pants off anybody." But neither the president nor Congress can afford to walk away from the new budget plan, since neither currently has an alternative for dealing with the fiscal dilemma into which they have put the country.

Congress, of course, has been talking bravely about curbing military spending and "freezing" everything else. But even before the president claimed scriptural sanction for his defense budget, the Pentagon had demonstrated how easily it could intimidate congressmen by the mere threat of closing a military base or cancelling a contract. As for a freeze, the president's plan would put much of the domestic budget in cold storage for years to come. And even so, the deficit would remain enormous.

True, the plan doesn't touch Social Security. But even if Congress extended its freeze to that sacrosanct territory -- and cut several billion from defense -- the savings would hardly offset the likely underestimate of deficits in the president's budget. In other words, Congress and the public must take the president's proposals seriously not because the cuts would solve the deficit problem, but because -- as military spending accelerates and interest on the debt compounds -- they are needed just to keep the deficit from getting worse.

That's why Congress, even at the risk of disrupting age-old log-rolling arrangements, has to get serious about taking on powerful regional and economic interests. It has to be willing to face down users of subsidized water and electricity; ow barges, yachts and planes; governors and mayors from affluent communities; corporate executives; small-business proprietors and, yes, even the tobacco lobby. And while it's at it, Congress ought to start taking on the even larger host of lobbies with a stake in preserving the present tax code.

Of course, while the president was conducting his highly successful reelection campaign, he didn't lay out the unpleasant cuts he is now calling for. In some cases, such as housing for the elderly, aid for college students and farm programs, he specifically affirmed his support for continuation or even expansion of programs now targeted for deep cuts. That's why House Speaker Tip O'Neill and other Democrats are quite right to call on the president to stop dealing in glittering generalities and begin educating the public on the details of his proposals.

There is no chance that the public will support Mr. Reagan's new plans unless he himself is willing to argue for them -- and not by invoking the supposed errors of the past or the rosy promises of the future, but by describing exactly what he is proposing and why.