The House Ways and Means Committee gave formal approval yesterday to the big Social Security financing bill, 23 to 14, but only after some last-minute politicking by Chairman Al Ullman (D-Ore.) and Joe D. Waggonner Jr. (D-LA.) won over a handful of reluctant Southern Democrats.

All the committee Republicans voted against the bill, which will face opposition on the floor because of the sizable payroll tax increases it would impose over the next 10 years.

The politicking involved agreement to seek a rule from the Rules Committee barring most floor amendments, but including among the limited number to be offered one strongly favored by several Southern Democrats.

Ullman, counting noses late Wednesday for yesterday's formal vote on reporting the bill, had concluded that the committee might reject the legislation if all dozen Republicans voted against the bill and were joined by five or six unhappy Democrats.

Waggonner, one of those unhappy with parts of the bill, came up with the solution: assure some of the hesitant Southerners that they would have an opportunity to offer a floor amendment to strip out a provision that would allow the Social Security trust funds to borrow from the treasury when they ran low. This authority is seen by some as a first step toward income-tax financing for Social Security.

Although Ullman was the original sponsor of this provision and the administration wants it, he gave in and on that basis Waggonner, J. J. Pickle (D-Tex.) and Omar Burleson (D-Tex.), according to committee sources, agreed to vote for the bill. Edgar L. Jenkins (D-Ga.) also swung over sources said, partly because a vote on the anti-borrowing was assurred and that the rule to be sought by the committee would allow him offer an amendment on payroll tax rates and wage bases.

With these votes added to those of Northern Democrats, Ullman then obtained the 23-to-14 endorsement of the bill.

Joseph L. Fisher (D-Va.) opposed the bill because it would bring government workers under Social Security in 1982 - and his district is full of government workers who don't like the idea.

The committee then voted to ask the RULES Committee to allow votes on only eight amendments including the anti-borrowing amendment, a Fisher amendment to strike out government worker coverage, and several GOP amendments to delay tax increases and reduce wage base levels - when the bill reaches the floor. Republicans say they don't like the committee bill because of too-quick tax increases and too-high wage base levels, which they claim will fall most heavily on middle-income workers.