A resourceful Senate yesterday proved it will stop at almost nothing when confronting the distasteful task of raising the government's debt ceiling.

It did not stop at Lebanon. It did not stop at Grenada. It did not stop at Cuba. In fact, about the only thing the Senate stopped at was discussion of the bill, which is needed by midnight Monday to keep the government from running out of borrowing authority.

Using the debt legislation as a springboard and never looking back, the Senate plunged into just about every other problem it could think of, even pausing for a moment to tweak the beard of Cuban Premier Fidel Castro, suggesting he could have back his troops captured on Grenada only if he also took back several thousand "undesirables" he let come here in the Mariel boatlift several years ago.

At the end of an exhaustive and even eloquent oratorical tour of the world's trouble spots, Finance Committee Chairman Robert J. Dole (R-Kan.), who sat glowering through most of the excursion, announced that the Senate would return to "germane amendments, if there are any germane amendments."

That did it for the day, unless one counts a short return trip to Lebanon and a brief flurry over a proposed nuclear freeze. The Senate quit after scheduling a rare Saturday session for today, ostensibly to come to grips with the debt bill. No one claimed to know when that might happen.

The bill, as drafted by the Finance Committee, would raise the debt ceiling from $1.389 trillion to $1.615 trillion, a figure already approved by the House. The increase, which would carry the government through next summer, is needed because the current limit is expected to be exceeded Tuesday, when the Treasury Department must turn over $13 billion to the Social Security system.

The Senate decided Thursday to cut the new total to $1.450 trillion, which the Treasury Department has estimated would last only through mid-February. This was done to put leverage on Congress and the Reagan administration to agree on deficit reductions in the meantime.

There is no sign of any agreement on the horizon, however. A plan offered Thursday by Dole to raise taxes by $56 billion and cut spending by $64 billion was rejected as "unacceptable" yesterday by the White House.

But if the Senate sticks by the reduced amount--and it indicated yesterday that it intended to do so--the bill will have to go back to the House, which is even more skittish than the Senate about debt ceiling increases. This could lead to futher complications in passage of the measure by the Monday deadline.

The closest the Senate came to dealing with the heart of the matter, which is budget deficits that are driving the debt to soaring new heights, was a proposal by Sen. Lawton Chiles (D-Fla.) to tie the debt ceiling increase to enforcement of the budget that Congress adopted earlier this year.

Under Chiles' proposal, the government's borrowing authority would run out again by Nov. 21 if congressional committees in the meantime do not approve a three-year package of $85.3 billion in tax increases and spending cuts, as the budget requires. The authority would run out again Dec. 21 if the legislation isn't enacted and signed into law by President Reagan.

The proposal was rejected, 53 to 31.

Chiles fared better, however, when he took on Castro and some of the people whom Castro shipped off to the United States, particularly including Florida, during the Mariel boatlift in 1980.

Declaring that the Cuban government "forced a large number of undesirable and often dangerous persons onto the United States," including 6,000 who are now confined in American prisons, Chiles' second resolution made this proposition: The U.S. would return Cuban nationals seized during the invasion of Grenada if Castro takes back the undesirables whom he sent north three years ago.

This nonbinding "sense of the Senate" resolution passed by voice vote without dissent.

The House and Senate handle their debt increase problems in different ways, neither of which can be found in civics books.

The House tucks its version of the increase into its budget resolution, where lawmakers hope it won't be noticed. The Senate resorts to no such subterfuge, but, more often than not, uses the debt legislation as hostage for other bills that can't get passed or signed into law in a more regular fashion.

Yesterday's session appeared to carry the Senate to new heights of legislative creativity. At one point, an exasperated Dole warned that the House-Senate conference on the bill might end up with him and House Ways and Means Chairman Dan Rostenkowski (D-Ill.) determining the country's foreign policy. On second thought, Dole added, "that may not be a drawback around here."