Senate Minority Leader Robert C. Byrd (D-W.Va.) yesterday called on Congress to begin drafting its own budget, setting off a rancorous partisan debate over budget compromise efforts that were reported to be approaching a critical phase at the White House.

"We're so close to either getting it or not getting it, it may not take much longer," said Senate Finance Committee Chairman Robert J. Dole (R-Kan.) in suggesting Byrd might be "torpedoing" the talks--a suggestion that provoked an angry denial from Byrd, who said he was only impatient for results.

Dole also said he heard that some Senate Democrats, whom he did not name, had urged their House counterparts in a meeting Wednesday not to reach agreement so the Democrats would have a sagging economy on which to capitalize in their effort to recapture the Senate in this fall's elections--again prompting an impassioned denial from Byrd.

"Totally, indubitably, unquestionably inaccurate," protested Byrd, who said he wants the talks to succeed but doesn't believe they can so long as President Reagan does not become actively involved.

In an attempt to avoid some of the impasse-points in the talks, the negotiators have begun discussing aggregate savings targets rather than specific deficit reduction measures, especially when they are unable to agree on specifics.

Under the target approach, the negotiators--and presumably Reagan and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.)--would agree to overall figures, or ranges of figures, for taxes and broad categories of spending. The specifics would be left to Congress when it enacted the budget and actual legislation to carry out the budget.

This would be a way of finessing the problems that have stalled the negotiators from the start, such as Reagan's refusal to abandon the third year of his tax cut and O'Neill's reluctance to tamper with Social Security. But some lawmakers contend it may not accomplish much outside of avoiding the embarrassment of a negotiating breakdown.

In another attempt to compromise the Social Security issue, House Democrats floated several proposals, including a three-month delay in payment of this summer's inflation adjustment for retirement benefits, during an evening session on Wednesday.

But it was withdrawn yesterday, according to a Republican negotiator, leaving unresolved the whole issue of cuts in basic benefit or entitlement programs.

The Democrats' Wednesday initiative, spearheaded by House Rules Committee Chairman Richard Bolling (D-Mo.), had briefly bouyed hopes for an agreement prompting Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) to claim that progress was finally being made.

But yesterday's session produced little progress, and once again the outlook was said to be gloomy.

Talks are scheduled to resume early today, with some Democratic as well as Republican participants saying they could break off if an agreement is not reached by the end of today's meeting. Baker, who is not in the negotiating group, had repeatedly said he would ask the Senate Budget Committee to begin drafting a budget of its own if an agreement could not be reached by week's end, although he indicated yesterday morning he might extend the deadline if progress was being made.

Bolling was reported by several sources to have suggested Wednesday night that Democrats might agree to a three-month delay in this summer's inflation adjustment for Social Security if Reagan would agree to take the lead in proposing it. However, Reagan has indicated he will not do so, and O'Neill has said he won't budge on the issue if Reagan won't.

O'Neill also assured a group of senior citizens representatives late yesterday that he would not accept a more ambitious proposal, discussed earlier by the negotiators, to impose a 4 percent cap on cost-of-living increases and have increases come every 15 months instead of the current 12. He was also reported to be cool to the idea of a three-month delay this year.

At a press conference earlier in the day, O'Neill tossed out the idea of taxing Social Security benefits of retirees with incomes of more than $20,000 a year. But other Democrats have opposed that approach, and it was never put on the bargaining table.

A Democratic proposal to help finance Social Security with general tax revenues, such as "sin taxes" on tobacco and alcohol, was rejected by Republican negotiators, O'Neill added.