Impatient that their high-level budget negotiations with the Reagan administration are still not producing results, Democratic congressional leaders said yesterday they will press forward with their own plans to reduce the federal deficit.

Senate Majority Leader Robert C. Byrd (D-W.Va.), expressing frustration at the slow pace of the budget talks and the administration team's lack of bargaining flexibility, said he would soon move to the Senate floor legislation raising $11.6 billion in new taxes that is the centerpiece of the Democratic deficit-reduction plan. The House last week passed its own $12 billion tax bill.

Byrd predicted that the budget negotiations now in their second week would not progress until Reagan is "wholeheartedly engaging in the discussion," and he urged the president to "give his negotiators the full freedom they need to close the agreement."

In addition, Byrd and House Speaker Jim Wright (D-Tex.) agreed yesterday they would speed up conference committee action on a number of individual appropriations bills so they could send them along to the president's desk. In the House, Wright and his leadership mapped out a schedule for passing a series of catch-all spending bills that might eventually be used to incorporate the rest of their deficit-reduction package if the budget talks fall through.

"The administration doesn't seem to understand the seriousness of it," said House Majority Whip Tony Coelho (D-Calif.) in explaining the Democratic strategy. "It sees the stock market crash as a passing fancy." Coelho said if the talks fail and the Congress has no back-up plans for reducing the deficit, the Reagan administration would be able to blame Democrats for the $23 billion in across-the-board cuts that would then be triggered by the revised balanced-budget law.

"What you have is an administration trying to pin the tail on the donkey," said Coelho.

The Democratic plans to move ahead on a parallel track came as congressional leaders and senior administration officials remained at loggerheads after a daylong series of meetings in the Capitol.

Yesterday's discussions centered on a plan jointly presented by the chairmen of the Senate and House budget committees, Sen. Lawton Chiles (D-Fla.) and Rep. William H. Gray III (D-Pa.), designed to reduce the deficit by about $31 billion this year and $46 billion in fiscal 1989.

Although lawmakers said that the Chiles-Gray proposal served a useful purpose in providing negotiators something concrete to discuss, the plan ran into immediate trouble on several fronts.

People familiar with the talks said that Republican senators feel it does not go far enough in cutting entitlement programs such as Medicare and farm subsidies that automatically confer benefits based on permanent law. In addition, the proposal was given "mixed reviews" by the administration, which has previously said it would agree to only $8 billion in new revenues.

Further, the plan was said to cause problems for some House Democrats who believe it treats defense spending too favorably.

Emerging from a luncheon meeting of Republican senators where the plan was reviewed, Senate Minority Leader Robert J. Dole (R-Kan.) said "it didn't go anywhere in here."

The Chiles-Gray plan would raise taxes by $10 billion and cut spending by another $10 billion -- most of it from domestic programs. It would raise another $11 billion from refinancing of Rural Electrification Administration loans, user fees, higher tax collections and lower interest on the national debt.

As yesterday's negotiating session broke up, Gray said "we are back talking and that's a positive sign. But we still have a way to go and time is running out."

Meanwhile, the president sought to dispel any impression that the budget talks have become deadlocked. Reagan, speaking as he named a new secretary of labor, said the stock market decline is a warning "we can't afford to ignore," and promised that the bipartisan budget negotiations would find a way to "put the public menace of deficit spending behind bars."

Some lawmakers expressed similar urgency on a day when the stock market suffered another drop of more than 50 points.

Bucking the current political climate, Senate Minority Whip Alan K. Simpson (R-Wyo.) urged his colleagues to consider cutting pension programs, even including Social Security, "for the same reason that Willie Sutton robbed banks: that's where the money is."

If Congress fails to respond to the market crash with a strong deficit-reduction package, said Simpson, "We would lose another notch in the eyes of the American public, and we're as low as quail crap already."