Senate Democrats, laying political groundwork for next week's showdown votes on a Republican deficit-reduction plan, tried unsuccessfully yesterday to put the Senate on record as opposing a proposed cutback in cost-of-living adjustments for Social Security recipients.

Minority Leader Robert C. Byrd (D-W.Va.) twice attempted to force a vote on a nonbinding resolution asserting the Senate's support for payment of full cost-of-living increases over the next three years.

He was blocked under routine parliamentary procedures by the Republican leadership, first by Majority Leader Robert J. Dole (R-Kan.) and then by Majority Whip Alan K. Simpson (R-Wyo.).

While the moves were largely symbolic, made without hope of success before a nearly empty chamber, they were seen as an attempt to underscore in advance that Democrats were giving top billing to Social Security and intending to lead the charge to prevent cutbacks.

Under a three-year deficit-reduction compromise worked out between Senate Republicans and the White House this month, Social Security beneficiaries would receive a 2 percent cost-of-living increase, along with compensation for inflation in excess of the anticipated rate, which is roughly 4 percent a year for the period. There would be no payment for inflation between 2 percent and the projected rate. Cost-of-living increases currently cover the full cost of inflation.

The proposal, which would save $3 billion next year and $22 billion over three years, is considered a cornerstone of the entire deficit-cutting plan and probably its most highly charged feature.

Many Republicans, still nursing election campaign wounds inflicted by Democrats on the Social Security issue, are highly skittish about having to vote to cut the inflation adjustment.

They have complained especially about reports that the cutback would drive thousands of older people into poverty.

Senate Republican leaders continued lobbying for GOP support of the overall package, which would cut spending by nearly $300 billion over the next three years to reduce deficits to less than $100 billion by fiscal 1988.

Meeting first with committee chairmen and then senators concerned with health program cuts, the leaders continued to hear appeals for modifications, according to Simpson.

At the same time yesterday, budget director David A. Stockman spiritedly defended President Reagan's budget-cutting proposals to out-of-town newspaper editors and television news directors at the White House, according to Knight-Ridder Newspapers. Stockman declared that Detroit Mayor Coleman A. Young and other mayors could absorb the loss of federal revenue sharing by freezing city employes' wages and cutting nonessential programs or, if they found that option distasteful, raising taxes.

Stockman called Miami's Metrorail system "a lemon" that illustrated why Washington should no longer subsidize construction of local mass transit projects.

It was learned that Chairman Dan Rostenkowski (D-Ill.) of the tax-writing House Ways and Means Committee plans to tell a Chicago business audience today that a minimum tax, proposed by many House members as a way to help reduce the deficit, is a "cop-out" if used as a substitute for far-reaching tax overhaul. A minimum tax does not deal with structural problems in the tax code, and special interests may back a minimum tax because they think they'll get a better deal from it than from an overall simplification, Rostenkowski will say.

A minimum tax "appears to satisfy the public demand for fairness without killing any of the most prized tax breaks," Rostenkowski says in prepared remarks. " . . . . It can be used to derail reform. It can provide a shield around the tax breaks we love to hate." Rostenkowski would consider a minimum tax only as a fallback, aides said.

But several members of his own committee are pushing minimum-tax legislation, including Reps. Marty Russo (D-Ill.) and Charles E. Schumer (D-N.Y.), who want a 25 percent minimum tax.

In the Senate yesterday, Sens. Daniel Patrick Moynihan (D-N.Y.) and John H. Chafee (R-R.I.) proposed a 15 percent minimum tax on individuals with income over $50,000 and on corporations with profits greater than $100,000. Monday, Sens. Lloyd Bentsen (D-Tex.) and John C. Danforth (R-Mo.) will introduce a 15 percent minimum tax for corporations earning more than $100,000. Sen. Howard M. Metzenbaum (D-Ohio) is the sponsor of a third plan.

Details vary, but the proposals essentially would limit the extent to which taxpayers could take certain deductions if the result reduced their tax rate too much. House Majority Leader James C. Wright Jr. (D-Tex.) said Wednesday that Democrats are looking at a minimum tax as a deficit-reducer.

However, some of the proposals, such as that of Bentsen and Danforth, would not raise federal revenue. Instead, corporate rates would be reduced to offset the higher tax take. The goal in those cases is to collect taxes from high-income corporations and individuals that have used tax preferences to pay little or no tax.