Drivers of the 105,000 cars and trucks that use the Woodrow Wilson Bridge over the Potomac every day are going to get a $60 million going-away present from the 96th Congress.

The House yesterday agreed to an amendment offered by Rep. Marjorie S. Holt (R-Md.) that provides for the federal government to pay the full cost of redecking the bridge.

The decrepit surface of the bridge, combined with the absene of any place for disabled vehicles to pull off, are responsible for frequent, massive backups on the six-lane, 5,900-foot span.

"All you have to do is listen to the traffic reports on the radio every morning to know about the constant problems," said Holt, who credited passage of her proposal by voice vote with "talking to the right people," and convincing House Democratic leaders that her idea had bipartisan support.

Normally, states pay 10 percent of the cost of repairing bridges on interstate highways in their jurisdictions, but Congress apparently agreed to pay the full cost of fixing up the Wilson bridge because it is the only federally owned bridge on an interstate in the country.

Besides, said Holt, "Maryland, Virginia and the District all said they didn't have money to come up with a matching share."

The three jurisdictions do share the $450,000 annual cost of operating the bridge: Maryland maintains the roadway; Virginia pays the electric bill and the District of Columbia operates the tower and draw span.

Work can begin as early as next spring, Holt said, because the preliminary planning already has been done by the Maryland Department of Highways. M. Slade Caltrider, Maryland highway administrator, said last summer that his state would be happy to arrange for the engineering and construction, if the federal government would come up with the money.

Rep. Herbert E. Harris (D-Va.) introduced legislation earlier this year to take care of that, but the bill never got out of the House Public Works subcommittee on transportation. One reason the bill may have died there was that the Carter administration never made up its mind what to do about it.

The Wilson bridge is the larger of two problems that face commuters who cross the Potomac here each day.

The other bridge in need of repair, the Cabin John -- officially the American Legion bridge -- would cost about $10 million to fix, and the financing has been assured as part of the regular 90-10 fomula for interstate highway structures, with Maryland, as owner, prepared to pay its $1 million share.

Both of the bridges are major bottlenecks because they require eight lanes of land-based traffic to feed into six-lane bridges, causing what Caltrider calls "the hour-glass effect."

Getting the money to fix the bridges will solve one of the headaches for traffic planners, but for some time the cure may be worse than the disease. Major repairs require closing portions of the bridges, further delaying movement of the vehicles that will cross the spans at the rate of 1.2 per second, 24 hours a day.

Together, the bridges link the Virginia and Maryland portions of the circumferential freeway known as the Capital Beltway, or Interstate 495. The Wilson, which connects Prince George's County with Alexandria, was completed 19 years ago this month, and the Cabin John, which links Montgomery County with Fairfax County, opened in 1963.

Holt's amendment was added to the huge Surface Transportation Act, which the House passed yesterday. The Senate is expected to agree to the House version before it adjourns this weekend.