With his showdown with House Democrats only two days away, President Reagan appealed directly to the voters on national television last night for his 33-month, 25 percent across-the-board income tax cut, contending its passage is essential to the restoration of the nation's economy.

"Our economic package is a closely knit, carefully constructed plan to restore America's economic strength and put our nation back on the road to prosperity," Reagan contended in a speech televised from the oval office. "Each part of this package is vital. It cannot be considered piece-meal. . . . Only if the Congress passes all of its major components does it have any real chance of success."

But Democrats instantly fired back at the president also on television. Rep. Ken Holland (S.C.), a member of the tax-writing Ways and Means Committee and one of the conservative southern Democrats who earlier supported the president on spending cuts but who is now sticking with his party on taxes, said, "I'm not going to vote for his tax package which lets the wealthly keep theirs and the working family keep right on shouldering the burden."

It is defections such as Holland's from the president's cause that have prompted Democrats to claim victory on the tax bill. House Speaker Thomas P. (Tip) O'Neill jr. (D-Mass.) said last night that only 14 Democrats are sure to support the president's tax bill with another seven or eight on the fence. This would give the Democrats victory by five or six votes.

However, the intensive White House lobbying for the measure, which included a weekend picnic at Camp David, is not over. Reagan saw 16 Democratic congressmen at the White House yesterday and more are due in today. White House officials acknowledge they are behind at this point but aren't conceding the vote.

O'Neill and House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) appeared on television immediately after the president's speech to denounce the Reagan plan as favoring taxpayers who make $50,000 or more a year.

"His bill is geared for the wealthy of America and that's what this fight is all about," O'Neill said.

The House is scheduled to choose Wednesday between the Reagan-backed measure and a 21-month, 15 percent cut backed by the Democrats. The Senate also is scheduled to act Wednesday, and differences will be ironed out in Congress.

In anticipation of the House vote, Reagan called upon his celebrated skills as a communicator to urge voters to lobby their congressmen on behalf of his plan, which the president called "the first real tax cut for everyone in almost 20 years." Throughout his speech, which he illustrated with charts, Reagan referred to the administration-conceived measure as "our bipartisan tax bill" because of its joint authorship by Rep. Barber Conable (R-N.Y.) and Rep. Kent Hance (D-Tex.)

"The majority leadership claims their [bill] gives a greater break to the worker than ours and it does -- that is, if you're only planning to live two more years," Reagan said. "The plain truth is our choice is not between two plans to reduce taxes, it is between a tax cut or a tax increase. There is built into our present system, including payroll Social Security taxes and the bracket creep I've mentioned, a 22 percent tax increase over the next three years."

The Democratic bill contains a trigger mechanism that would provide for a third-year tax cut, but Reagan said there was "sleight-of-hand in that trigger mechanism" because the deficit would be so great that it would never come into play.

"Incidentally, their claim that cutting taxes for individuals for as much as three years ahead is risky rings a little hollow when you realize that their bill calls for business tax cuts for seven years ahead," the president said.

The president had also planned to talk about Social Security amendments in his speech but backed off at the request of GOP congressional leaders, who fear that the president and the Republican Party are vulnerable on this issue. Reagan, who has proposed large benefit cuts for future Social Security recipients, tried to address this concern in one of the opening passages of his message, saying:

"I stated during the campaign and I repeat now I will not stand by and see those of you who are dependent on Social Security deprived of your benefits. I make that pledge to you as your president. You have no reason to be frightened. . . . In any plan to restore fiscal integrity of Social Security I personally will see that no part of the plan will be at the expense of you who are now dependent on your monthly Social Security checks."

Earlier this year, Reagan proposed changes in the system that would have phased out the $122-a-month minimum Social Security benefit.

Speaking of the tax measure, Reagan said "our bill includes just about everything to help the economy." What he did not say was that many of the provisions he went on to cite had been put in the legislation in a bidding war to obtain Democratic House votes.

These provisions include a reduction in the so-called marriage penalty, under which two workers pay higher taxes if married than they would if single; big cuts in taxes paid by the oil industry and business generally; "savings incentives" in the form of tax forgiveness on interest income, sought by the savings and loan estate tax, one of which would eliminate that tax entirely for surviving spouses.

"No longer, for example, will a widow have to sell the family source of income to pay a tax on her husband's death," Reagan said of this provision.

Reagan's attack on the Democrats from the quiet santuary of the Oval Office was more biting and less conciliatory than the appeals he had made for his budget on Capitol Hill.

"Our opponents in the beginning didn't want a tax bill at all," he said. "What is the purpose behind their change of heart? They've put a tax program together for one reason only, to provide themselves a political victory.

"Never mind that it won't solve the economic problems confronting our country. Never mind that it won't get the wheels of industry turning again or eliminate the inflation which is eating us alive. This is not the time for political fun and games. This is the time for a new beginning."

Holland, a "boll weevil" Democrat who represents a congressional district with a median annual income of $15,000, was one of several Democrats to appear on TV to reply for his party. He attacked the Reagan plan as a tax relief proposal for the rich.

"It would be pretty tough to vote for the president's tax bill and be blamed for a giving a $22,000 tax cut to the average guy making over $200,000," Holland said. "It would be impossible for me to vote for a plan that gives no cut at all to families earning less than $20,000 -- after the impact of inflation and payroll tax increases."

Joining Holland in response to the president's speech, Rep. Richard Gephardt (D-Mo.), also a member of the Ways and Means Committee, asked a series of rhetorical questions directed to the same point.

"Have the rich who earn more than $50,000 been the biggest victims of inflation and Social Security tax increases in recent years?" he asked. "Have they suffered more than the average, middle-income working American?"

And Sen. Bill Bradley (D-N.J.), chairman of an ad hoc Democratic Senate panel on budgets and tax cuts, said that the three-year commitment of the Reagan plan was too extensive because the administration couldn't even predict the state of the economy six months from now.

"It is clearly an experimental plan," Bradley said. "It gambles with the only economy we have."