House-Senate budget conferees got off to a slow start yesterday, with Republicans haggling into the evening among themselves over spending differences and over whether next year's deficit can be kept under $100 billion.

At issue, among other things, was a claim by some House Republicans that any major changes in the House-approved budget, including its projected deficit of just under $100 billion, would jeopardize chances for House concurrence in any compromise from the conference.

As the Republicans broke up, they were reportedly exploring a compromise with a deficit of about $103 billion.

In an opening statement that pleaded for flexibility, Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) warned that the conference, despite seemingly narrow differences between the House and Senate versions of the budget, could nonetheless collapse over projected deficits and other problems.

"We cannot allow ourselves to be so inflexible that we are stymied by a symbolic deficit target," he said in an oblique warning to the House Republicans.

Sen. Ernest F. Hollings (S.C.), ranking Democrat on the Senate committee, was more explicit than Domenici, asserting it is "totally unrealistic" to assume that a deficit of less than $100 billion is attainable.

Rep. Delbert L. Latta (Ohio), ranking Republican on the House Budget Committee and chief sponsor of the House plan, shot back that it would be attainable if the Senate conferees simply agreed to go along with the House version.

The House budget calls for a deficit of $99.3 billion for the 1983 fiscal year starting Oct. 1, although the nonpartisan Congressional Budget Office has said it actually would entail a deficit of nearly $110 billion. The Senate budget anticipates a deficit of $116 billion, although CBO officials say the Senate's deficit may now be somewhat less.

The deficit projections are viewed as perhaps the major hang-up for the conference, along with assorted substantive differences in such areas as cost-of-living increases for retirement benefits other than Social Security, domestic appropriations levels, foreign aid, proposed cuts in benefit programs for the poor and, to a lesser extent, tax increases.

One major difference is that the House cuts more deeply into programs for the poor, while the Senate's cuts are spread out more evenly, including anticipated but unspecified savings from Social Security after a presidential commission makes recommendations later this year on how to keep the huge retirement fund solvent.

Both budgets propose tax increases of at least $20 billion this year, for an overall total of about $100 billion by 1985. But the House wants to require action this year on only one year's worth of increases, while the Senate wants to nail down all three years' worth this year.

In his opening remarks to the conference, which will reconvene today, House Budget Committee chairman James R. Jones (D-Okla.) characterized the dispute as involving a choice between two Republican-drafted budgets, both of which have been endorsed by President Reagan.

It's "almost a family matter within the Republican Party," that Democrats can do little more than mediate, Jones said.

Meanwhile, on the related issue of a supplemental appropriations bill for the rest of the current fiscal year ending Sept. 30, the Reagan administration, in a letter from Office of Management and Budget Director David A. Stockman to congressional leaders, formally urged rejection of a House-Senate conferees' compromise on grounds that it is too expensive.

Stockman cited a $3 billion housing "bail-out" plan as "particularly unacceptable" and also objected to $1.3 billion for other programs. If the bill is not stripped back, it would be hard for the president's advisers to recommend that he sign it, Stockman said.