The sharp clash earlier this week between the speaker of the House and the chairman of the Ways and Means Committee--dismissed by participants as a Democratic family squabble--reflects a fundamental disagreement over tactics that will color the debate over budget and tax issues this year.

The conflict focused on a speech by Rep. Dan Rostenkowski (D-Ill.), the chairman, in which he signaled a willingness to abandon the Democratic fight to modify the third phase of the administration's tax cut, the 10 percent rate reduction on July 1.

The suggestion infuriated Thomas P. (Tip) O'Neill Jr. (D-Mass.), who is intent on using the tax cut as a vehicle to stress the "fairness issue": the Democratic contention that the Reagan administration's program is designed to help the rich at the expense of the poor.

"It's the fairness issue. We are going to keep working on a fairness program," O'Neill said yesterday. "I can't give that up." With this in mind, O'Neill and most of the rest of the Democratic leadership, House and Senate, intend to force votes on proposals to restrict the tax benefits going to those making more than $50,000 a year, the income group that benefited most from the administration's tax cut.

At issue between Rostenkowski and O'Neill is a basic question: Should Democrats who have gained firm control of the House adopt a posture of compromise and negotiation, or press issues that will produce ideological confrontations between the two parties and focus public attention on the differences between Democrats and Republicans.

For O'Neill, the choice has been in favor of staking out a fundamentally liberal Democratic posture in contrast to the GOP. In addition to his own philosophic agreement with that posture, he is convinced public perception of the differences between the parties is the reason Democrats picked up 26 seats in 1982.

Referring to the 1981 and 1982 sessions, O'Neill said "it was easy for us to acquiesce. We weren't going to win. But this year we are going to have some victories." Referring to Rostenkowski's speech, he said "the leadership has got to be in on policy before they make speeches."

Although the two senior Democrats are close friends, their differences over tactics are significant in that O'Neill is the defacto head of the Democratic Party, while Rostenkowski is in charge of the committee with jurisdiction over almost every key spending and tax issue, except defense.

Rostenkowski, in growing contrast to O'Neill, repeatedly has shown a willingness to work with and compromise with the administration, not only on the tax issue, but such key partisan subjects as Social Security and the entire budget process.

"Rostenkowski views the president as his boss," a member of Congress close to both O'Neill and Rostenkowski said. "He thinks he can work with them the White House ." He said that O'Neill "has come to the conclusion that these guys the Reagan administration don't want to do what's right."

Since the early days of the Reagan administration, Rostenkowski has sought to avoid head-on conflict with the White House. During consideration of the 1981 tax cut, he tried unsuccessfully to negotiate a compromise. Throughout the Social Security debate, he was prepared early on to develop a bipartisan solution, willing to accept more of the GOP demands for benefit cuts, as opposed to tax increases, than other key Democratic leaders.

Perhaps epitomizing the favored Rostenkowski approach was the attempt last year by Republican and Democratic congressional leaders, along with administration officials--collectively known as the "Gang of 17"--to privately work out a comprehensive budget package.

"Instead of political confrontation, Danny would prefer to settle things behind closed doors," a close associate said. "Danny thinks that when there is common ground, why slam the door in the administration's face."

In this light, White House officials see Rostenkowski as far more "reasonable" than most other members of the Democratic leadership, and, in private, some Republican strategists yesterday indicated they hope to be able to exploit the differences in tactics and style between Rostenkowski and O'Neill.