Ronald Reagan's second term is under way, its anti-government rhetoric intact, even if the rhetoric defies the reality of what has taken place in the past four years.

In 1981, the president summed up his philosophy by saying, "Government is not the solution to our problem. Government is the problem."

Sworn in for a second term on Monday, Reagan recalled the thrust of his first Inaugural Address, and added: "We believed then and now: There are no limits to growth and human progress, when men and women are free to follow their dreams. And we were right to believe that. Tax rates have been reduced, inflation cut dramatically, and more people are employed today than ever before in our history."

Against the glow of the current economic euphoria and a rising stock market, few voices were raised this week to challenge a popular and gracious president. But what he failed to say, as he decried big government, is that in his term the national government has grown bigger than ever; the national debt has doubled -- from roughly $900 billion to $1.8 trillion; and the federal budget deficit is spinning out of control.

The best that his lieutenants are ready to prognosticate is that the deficit might be cut to $130 billion by fiscal 1988. And as an astute observer, Charls Walker, points out, a continuation of good economic statistics and a rising Dow-Jones index "could dampen political enthusiasm for deficit reduction."

Yet, if there are no changes in policy, the fiscal 1988 deficit could be $230 billion to $240 billion, and the national debt by that time may have grown to $2.5 trillion.

A careful listener to the president's recitation on Monday inaugural heard him say: "We have begun . . . to reduce the increase in the cost and size of government nd its interference in people's lives." The operative words are "reduce the increase." The claim, in other words, is only that the government isn't getting bloated as fast as before, not that government has gotten smaller.

"The Reagan Record," an assessment by the nonprofit Urban Institute last year, noted that when Reagan took office he promised to slash domestic spending from 23.5 percent of the gross national product in fiscal 1981 to 19 percent.

Despite the axe swung at social programs, the administration actually boosted the federal government share of GNP to more than 24 percent for fiscal 1985, the result of defense program increases that almost offset the domestic cuts, plus the effects of enormously high interest charges on the swelling debt.

At best, the budget for fiscal 1986 to be announced in a few days will only cut the government share of GNP to about 23 percent -- or roughly where it was when Reagan took offic.

Said the president in his Inaugural Address, "We have come to a turning point, a moment for hard decisions. I have asked the Cabinet and staff a question and now I put the same question to all of you. If not us, who? And if not now, when? It must be done by all of us, going forward with a program aimed at reaching a balanced budget. We can then begin reducing the national debt."

But the president's actual proposal is painfully inadequate. The original Reagan goal of getting the fiscal 1988 deficit down to $100 billion has been scrapped. And a tax increase is still verboten, as was reiterated in weekend television appearances by Treasury secretary-designate James Baker III. Reagan's deficit-reduction effort will be largely limited to a "freeze" for fiscal 1986, mostly on domestic programs. Defense spending comes off almost unscathed -- just a token cut of $8.7 billion for fiscal 1986.

According to chief of staff-designate Donald T. Regan, the president's budget will call for $50 billion in spending cuts from the $200-$230 billion totals that the new budget otherwise would reach. That would cut the deficit in fiscal 1986 to a range of $170 billion to $180 billion. "Fifty billion in the first year translates into about $90 billion three years afterward," Regan said.

There is one thing clear from all of this: If there is to be meaningful deficit reduction, Congress will have to take the issue out of the president's hands, and hit the defense pro- gram harder. That's the only way in which House Democrats can be persuaded to justify a vote to freeze the non-defense parts of the budget.

For Senate Republicans, as Walker suggests, the risk is that euphoria over the economy will not last forever. If interest rates rise, or the economy slips in 1986, the deficit will have to be tackled in a crisis atmosphere just ahead of what promises to be a tight political struggle for control of the Senate.