The Senate gave final approval yesterday to President Reagan's proposed $50 billion increase in the debt ceiling as Democrats, still smarting from being labeled big spenders for shouldering the debt burden in the past, forced reluctant Republicans to provide the margin of victory.

Despite hours of political posturing and a handful of threatened amendments, Reagan's proposal to raise the borrowing limit from $935 billion to $985 billion was approved 73 to 18, an even bigger margin than the House provided Thursday in approving the measure 305 to 104.

It was Reagan's first legislative victory in Congress, but it came at the price of a pound of political flesh from the new Republican majority in the Senate, many of whose members had been proud to say in the past that they had never voted for a debt ceiling increase.

Wearing what Sen. William L. Armstrong (R-Colo.) called a "smirky demeanor," the Democrats appeared to enjoy every minute of their little drama -- even though they failed, 52 to 41, in an effort earlier in the day to keep the increase to $28 billion.

As the roll call began, the Democrats voted against the debt bill, almost to a man, forcing Republican after Republican to cough up a painful "yes" vote.

Only after Senate Minority Leader Robert C. Byrd (D-W. Va.) was sure that Republican votes had put the measure over the top did he lead a vote-switching parade in which about two dozen Democrats jumped to their feet and changed their votes.

Some, including bruised veterans of recent campaigns who were still nursing grudges over the big-spender charge from GOP opponents, switched with solemnity. Others, such as Henry M. Jackson (D-Wash.), who managed in the confusion to vote yes, then no and then yes again, grinned, danced a little jig and waved at the press gallery. As the bill passed, Majority Leader Howard H. Baker Jr. (R-Tenn.) emitted a long "whew!"

In the end, three Republicans (Armstrong, Mack Mattingly of Georgia and John P. East of North Carolina) voted against the measure, along with 24 Democrats of both liberal and conservative persuasion and Sen. Harry F. Byrd Jr. (Ind-Va.). No other Washington area senator voted against it.

Republican floor leaders for the bill tried to make the bitter pill easier to swallow. "I just suggest we support the president on this . . .," said Senate Finance Committee Chairman Bob Dole (R-Kan.), adding that any blame for the nation's mounting debt rested with the Carter administration and previous, Democratic-controlled Congresses.

Not so, the Democrats responded. Regardless of party or philosophy, "there is not a member of this body who hasn't supped at the trough of fiscal irresponsibility," claimed Sen. Dale Bumpers (D-Ark.), noting that a Democratic-controlled Congress had to raise the debt ceiling after the Ford administration left office in 1977.

With Congress facing a Lincoln's Birthday recess between now and the time the current debt ceiling is likely to be breached around Feb. 18, several proposed amendments that could have delayed passage were withdrawn.

Among them were a proposal from Sen. Roger W. Jepsen (R-Iowa) to ban all trade with the Soviet Union as long as the year-old embargo on grain sales continued, and a proposal from Sen. Howard M. Metzenbaum (D-Ohio) to reinstate the price controls on crude oil that Reagan removed last month.

Sen. James A. McClure (R-Idaho) also introduced and then withdrew an amendment to raise the debt ceiling to slightly more than $1 trillion, which he said would be enough to last through next year. McClure's amendment would have had the added effect of shielding Reagan from having to acknowledge a trillion-dollar debt later in his administration, long after the Republicans could conveniently continue to blame Carter. Reagan had reportedly considered such a step but rejected it as difficult to sell Congress at this time.

As it is, the debt ceiling will probably have to be raised again -- probably past the $1 trillion mark -- by September, according to administration officials. Legislation to raise the debt ceiling is needed periodically so the government can continue to borrow money to finance its obligations and day-to-day operations.

At the end of the vote, a group of conservative Republicans led by Sens. Jesse Helms (N.C.) and Orrin G. Hatch (Utah) introduced a "sense of the Senate" resolution urging that no further debt ceiling increases be approved until Congress revises its budget procedures to include such controversial steps as reinstating the president's power to impound congressional appropriations. Other proposals include establishing binding spending ceilings and consideration of a constitutional amendment to require balanced budgets.