Senate and House Democratic leaders, decrying the nation's new 10.8 percent unemployment rate as a "national disgrace" and a harbinger of an economic depression, responded yesterday with separate and conflicting programs to double the size of the administration-backed jobs initiative in the lame-duck session of Congress.

They were supported by AFL-CIO President Lane Kirkland, who warned of possible "turmoil in the streets," and Democratic National Chairman Charles T. Manatt, whose terse message for President Reagan, on tour in Latin America, was: "Mr. President, phone home."

Reagan, however, while describing the latest unemployment increase as a "continuing tragedy," stuck by his insistence that Congress work with the administration to bring about recovery by less spending, not more.

Although they differ significantly in content, both the House and Senate Democratic proposals would spend a total of about $10 billion and provide about 650,000 jobs.

This is roughly twice what Reagan is supporting in a bipartisan $5.5 billion plan to finance highway, bridge and mass transit work by a 5-cent-a-gallon increase in the federal gasoline tax.

While Republicans continued to oppose major jobs initiatives this year and warn of a presidential veto, Senate leadership sources indicated some additional jobs spending might win GOP approval, including funding of water and sewer projects and improvements for veterans hospitals.

The House Democratic plan embraces the gasoline tax to finance highway-related projects and would add another $5 billion for other public works improvements, presumably to be financed by adding to the projected deficit of at least $170 billion for fiscal 1983.

The Senate Democrats' plan, drafted by a 14-member task force for submission on Tuesday to the Senate Democratic caucus, shuns the administration-backed approach and includes some curtailment of next July's tax cut for those in the upper-income brackets as one of several financing options that include a gasoline tax increase.

The income cap in the Senate plan would phase down the 10 percent income tax cut for individuals making more than $46,500 a year and eliminate it for all who make more than $78,600.

The plans surfaced as Senate Minority Leader Robert C. Byrd (D-W.Va.) called the 10.8 percent November jobless rate a "national disgrace that need not have been," and House Majority Leader James C. Wright Jr. (D-Tex.) said the recession has "taken on the dimensions of a depression."

Kirkland said that, while he would regret violence, "if all else fails and then people come to the conclusion that the only way . . . is to create turmoil in the streets, well, then, I guess perhaps we have to go out and organize some turmoil in the streets."

Reagan, en route from Brazil to Colombia, said the administration has laid the groundwork for recovery by policies that have led to less inflation, lower interest rates and other signs of economic recovery.

"In the meantime it is imperative that the Congress and the executive branch work closely and constructively together to hold down spending and encourage economic growth," Reagan said.

He added that he is encouraged by congressional progress on the highway measure and hopes for prompt action on his "enterprise zone" legislation to encourage business investment in decaying neighborhoods.

Senate Majority Whip Ted Stevens (R-Alaska) speculated that Republicans might support more jobs for highway-related work than the administration wants but added, "We can't go back to temporary solutions." The answer is not in "increasing the burden on those who are working now," he added.

As proposed by the task force, the Senate plan calls for $6 billion in major repair work that can be started within 120 days, including $3 billion for highways, $1 billion for bridges, $1 billion for mass transit and $1 billion for sewers, water supply lines and pumping stations.

Another major component is $2 billion in six-month public works jobs for less skilled workers, allocated to state and local governments on the basis of local unemployment rates. Work would range from rust-proofing bridges to repairing fire hydrants. Most workers would have to have been unemployed at least 15 of the last 26 weeks. Jobs would be available within 90 days.

Another $1 billion would be provided for supplemental unemployment benefits, job retraining, employment of older people, reforestation, public housing rehabilitation and coal mine reclamation. The extra jobless benefits would add from two to five weeks of unemployment assistance to levels approved earlier this year.

House Democrats, who intend to make their plan part of an omnibus "continuing resolution" for financing the government, were less explicit in a statement released yesterday after the latest in a series of leadership meetings on the issue.

They said they intend to spend $5 billion to expand existing federal and local public works programs, with special aid for high-unemployment areas. Rehabilitation of federal buildings and veterans hospitals, weatherization aid to local governments for low-income housing and state-administered job training programs would also benefit.

Although the House Democrats have yet to nail down their plan, including dollar amounts for its components, Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said he thought it would "get a big vote in the House," enough to convince the Republican leadership in the Senate to approve at least part of it.