One day last week, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) welcomed to his office on Capitol Hill a large group of his fellow democrats, many of them relatively junior members of the House. The visitors wanted to talk to O'Neill about the coming 97th Congress and their hopes for a larger role in the Democratic leadership.

There is nothing unusual about Democratic House members meeting with the Democratic speaker. What made this meeting notworthy was the makeup of the visiting contingent and what this may signal about the likely direction of the new House, nominally the surviving bastion of Democratic control in the federal government.

O'Neill's visitors were all conservative Democrats, most of them from the South and Southwest. In the wake of the Republican election victories, they have correctly sensed that they have a new importance, organized themselves to exploit it and begun to flex some newfound political muscle. In granting them an audience, O'Neill, an old style liberal never known for solicitude toward his conservative Democratic brethren, was simply beginning to accommodate himself to a new political reality -- on Nov. 4 the Democrats not only lost the White House and control of the Senate, they also lost all but a paper majority in the House.

The Democrats will retain numerical control of the new House with a 26-vote majority. But on any number of issues, effective control of the House will be beyond the grasp of the Democratic leadership. All the ingredients of a bipartisan conservative coalition sympathetic to the objectives of President-elect Ronald Reagan will be present, and in many instances the bloc of conservative Democrats who visited O'Neill last week will hold the balance of power. What this will mean in specific programs and pieces of legislation is impossible to say. But this much is already clear: not only in the GOP-controlled Senate but in the House as well, Reagan will find working majorities willing to back his desire to increase defense spending while attempting to move toward a balanced budget by cutting domestic programs.

The new administration's opportunities in the House are written in the numbers from Nov. 4.

In the last Congress, the Democrats enjoyed an almost 2 to 1 majority and, assuming Republican solidarity, it took some 60 defections from Democratic ranks to defeat the leadership. The number of defections, according to House officials, ranged between 30 to 50 votes depending on the issue, meaning that in most cases O'Neill and the other Democratic leaders could deliver.

But in the new Congress it will take only 26 defections for the Democrats to lose their majority, again assuming Republican solidarity. And within the nominal Democratic majority that exists on paper, there are more than 26 Democrats like Texan Charles W. Stenholm of Abilene, a conservative budget cutter who sees eye to eye with the Republicans on many issues and who, along with other members of the Democratic Conservative Forum, paid his respects to the speaker last week.

Stenholm, the head of the group, said the Conservative Forum now has 34 members and that he expects it to number more than 40 by the time House Democrats get down to organizational meetings next month.

"Our intent is to moderate our party," he said. "We feel the American people spoke very loudly on Nov. 4 and if we're not successful in moderating our party we'll be the minority party in the House as well."

Stenholm and his allies have set as their first objective a larger role for themselves in the House leadership itself. They have submitted to O'Neill and Majority Leader Jim Wright (Tex.) their nominees for majority whip, a job for which Rep. Dan Rostenkowski (Ill.) is in line but which he may pass up in order to assume the chair of the Ways and Means Committee.

The conservative Democrats are also pressing O'Neill for more representation on the Democratic Steering and Policy Committee and the Budget Committee and, to a lesser extent, the Ways and Means and Appropriations committees.

But the Conservative Forum's ambitions extend beyond organizational matters to substantive issues on which they may well hold the balance of power. mStenholm said he intends to have in place for the new Congress his own whip system to hold the Conservative Forum together on key issues. "On issues that we feel strongly about, if we can be the majority or the swing vote, that's exactly what we want to do," he said.

Beyond a desire to strengthen the military, cut federal spending, and reduce the role of the federal government in America life-all general objectives also espoused by Reagan -- it is difficult to pinpoint the issues on which the conservative Democrats will attempt to exert their new influence. But one clue to their thinking on the budget may lie in the recommendations of the Bipartisan Coalition for Fiscal Responsibility, a group that included Stenholm, Rep. Phil Gramm, another Texas Democrat, and other members of the Conservative Forum.

The coalition proposed $26.3 billion in budget cuts for the fiscal year that began Oct. 1. The proposed cuts included $2.4 billion from general revenue sharing to the states, $3.9 billion from CETA public service jobs, $1.1 billion from food stamps, $2 billion from unemployment benefits, $1 billion from foreign and multilateral aid and $1.9 billion from various education, social services and antipoverty programs.

On other key notes in the 96th Congress, members of the Conservative Forum generally favored higher defense spending and the deregulation of natural gas prices, but opposed creation of a Consumer Protection Agency and federal funding for abortions. Many of them are from farming districts and are sympathetic to demands for propping up agriculture prices.

What may most distinguish these conservative Democrats from House Republicans, according to one House source, is their attitude toward tax policy. While they may go along enthusiastically with Reagan proposals to slash domestic spending, they are not as enthusiastic as their GOP colleagues toward Reagan's support for the Kemp-Roth tax cut measure, beginning with a 10 percent tax cut next year.

O'Neill and other House liberals are, of course, well aware of the new political realities on the Hill. Unsure of having a real majority on key issues, the speaker already has been talking of giving the new president "a lot of rope" in the next Congress as the Democratic leadership assumes an essentially defensive position. There was already a trend toward more conservatism in the House, and the Nov. 4 election and the formation of the Conservative Forum will serve to accelerate it.

"There is no question that they feel buoyed by the election, "an official close to O'Neill said of the conservative Democrats. "They have influence and they plan to exercise it. . . . Forces around here tend to get accommodated."