Buoyed by surprise House approval of a similar measure Wednesday, the Senate Appropriations Committee yesterday approved and sent to the floor a measure authorizing $49 million to restore the crumbling West Front of the U.S. Capitol.

Committee Chairman Mark O. Hatfield (R-Ore.) expressed gratitude that the action by the House of Representatives broke a deadlock of nearly 20 years between the House and Senate over whether to preserve or extend the deteriorating, age-weakened wall, which last month shed a 16-foot-long section of sandstone onto the lawn below.

He himself supported extension from the beginning, Hatfield said, but, like the House majority that voted for restoration Wednesday, "had yielded to the obstinance of those opposing it in order to get something done."

The full Senate is expected to give speedy approval to the measure when it reconvenes June 8 after the Memorial Day recess. Actual work on the wall could begin as early as this summer.

The Senate bill exceeds that passed by the House by roughly $1 million--a difference legislative subcommittee chairman Sen. Alfonse M. D'Amato (R-N.Y.) said involved work primarily on the marble terraces adjacent to the West Front.

He said he did not expect that to be a point of major contention in the conference committee. A greater potential issue, he said, is control of the project, including Senate insistence on a fixed-price contract and a performance bond from any contractor.

Some House leaders have "reservations" about that language, he said, while senators have reservations about the cost-control effectiveness of George M. White, architect of the Capitol.

"Mr. White's track record, particularly on the Hart (Senate Office) Building, is hardly one to inspire confidence," D'Amato said.

White, who serves at the pleasure of the president and was appointed by President Nixon in 1971, may be the victim of more than criticism. The West Front extension proposal was marketed as a way to add 147,000 square feet of badly needed office space for congressional use.

But several speakers in the House debate Wednesday noted that White himself occupies 22,000 square feet of prime space in the Capitol, with a mini-empire of 160 supporting staff members, and has never provided a requested analysis of ways to use existing space in the building more efficiently.

With the extension proposal dead, several House members said yesterday, the House leadership may move to reclaim at least part of the architect of the Capitol's office space and transfer displaced staffers to other less desirable buildings.

The Senate measure approved in committee yesterday largely favors a restoration program for the West Front recommended in March 1978 by Ammann and Whitney, a New York firm of consulting engineers. It would beef up and moisture-proof the West Front's foundation, reinforce the walls above with stainless steel rods, renovate inoperable windows and birdproof the entire structure in the face of the Capitol's ubiquitous pigeons.

It would dismantle and reconstruct the portico with new columns, and repair and reinforce broken ballustrades as well as the roof and supporting beams over the north central attic.

The entire sandstone face would be cleaned of some 40 coats of paint accumulated over the years and renovated where necessary with new sandstone or limestone facing coated with a durable preservative.

While some voices have been raised in favor of replacing the existing sandstone with marble, preservationists warned yesterday that such a substitution would quickly escalate the cost of the project beyond the funds appropriated by either the House or Senate bills.

D'Amato said it is the intent of the Senate bill to concentrate on the structural needs of the West Front in saving it from further deterioration.

Although the bill provides a 25 percent contingency provision for presently unknown difficulties discovered during the restoration process, he said additional funds might still be needed "for ornamental work--work we don't have to do but might like to do."

He said he believes such costs could be met by public subscription rather than tax funds.

"I believe the American public would be very generous in making available funds for their Capitol," he said. "I think we might all be very pleasantly surprised."