House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), unusually conciliatory toward President Reagan since the November elections, resumed the attack yesterday, accusing Reagan of not being "honest with the American people" in his State of the Union address Wednesday night, particularly about the federal budget deficits.

At the same time, many Democrats were dismayed and angered by their party's half-hour televised response to the president's speech.

The response was intended to demonstrate that the party is alive and well despite Reagan's landslide reelection and is trying to listen to the people and learn from its mistakes. Many Democrats, however, complained that much of the program was a "pandering" to those who want the party to become a mirror image of the Republicans and did not outline Democratic budget and tax proposals.

O'Neill, 72, said at a news conference yesterday that the Democratic response was deliberately easy on Reagan because "we did not want to hurt this kindly old man that America loves on his 74th birthday." He referred to Reagan several times as "an old man" and "a kindly old man," in a lighthearted way.

He charged, however, that Reagan has "mesmerized" and misled the American people about who is responsible for the budget deficit, and he particularly disputed Reagan's assertion that the deficit is the result of "nearly 50 years of government's living beyond its means."

"That clever rhetoric covers up the facts," O'Neill said. "In 1981, when President Reagan took office, the national debt was just over $900 billion. Today it is $1.8 trillion, double what it was when he took office . . . . The debt will be $3 trillion when he leaves office, triple what it was when the Reagan revolution began."

He urged the president to "start with the facts.

"Let us work hard to cut the deficit, Mr. President, but . . . do not point the finger at the distant past when you yourself have so much responsibility for these deficits resting on your own shoulders."

Many Democrats said they thought their party's response immediately after the president's speech on NBC and CBS -- ABC, which ran "Dynasty" instead, carried the response last night -- showed too many people being complimentary of Reagan's first-term accomplishments.

"I don't understand why we run something the Republicans should pay for," said former Democratic national chairman John White. "I ran into Jim Lake the Reagan-Bush campaign press secretary at lunch and he started laughing and said that Frank Fahrenkopf chairman of the Republican National Committee was busy writing checks for the people who produced it."

Frank Mankiewicz, a former adviser to the Kennedy family and George McGovern's 1972 campaign manager, noted that the response reportedly cost about $100,000.

"I would have responded to a party fund-raising appeal to raise $100,000 to keep it off the air," he said. "I don't know why we didn't see any of the party leaders on it -- Gov. Mario Cuomo of New York , Sen. Gary Hart D-Colo. or Sen. Ted Kennedy D-Mass. ."

Several Democrats complained that the program -- televised in "focus groups" in four cities -- began with people praising Reagan and criticizing Walter F. Mondale's proposal to raise taxes to control deficits.

"Why didn't we take credit for where we're going on tax reform?" asked one. "We could have laid out the Bradley-Gephardt tax revision plan, showed the domestic programs we'd save and what we'd cut out of the defense budget."

Not everyone was critical, however.

"There's not much you can do to compete with the high drama of this president," said Robert S. Strauss, another former national chairman. "The response was solid, not emotional. It was different. There were new faces. They were saying new things. I liked that."

Raymond D. Strother, who produced the response, said he used the focus groups in Kansas City, Philadelphia, Denver and Rockville, Md., in an attempt to win back wayward Democrats and appeal to independents.

"We were trying to establish a bond with a group we're losing, the upwardly mobile group in their 40s," he said. "We're trying to generate enthusiasm with those who call themselves independents rather than Democrats at cocktail parties.

"We tried to counter the talk that the party is going out of existence by pointing out how many governors and House members and state legislators we have elected. We need to develop new techniques if we're going to win the country back."