HAVING EARLIER voted for a long overdue restoration of the West Front of the Capitol building, the Senate will have a chance today to vote for an additional measure that will help keep the restoration on time and within budget. The measure in question is an amendment proposed by Sen. Alfonse D'Amato (R-N.Y.). The senator wants to be sure that, as the project gets under way, someone is keeping a trained eye on the activities of Mr. George M. White, the Architect of the Capitol.

As Sen. D'Amato notes in remarks quoted in the For the Record column today, Mr. White is a busy man. He supervises a staff of more than 2,000 employees who make sure that the official buildings of Capitol Hill and their surroundings meet the high standards of Congress. Many of Mr. White's works are admirable--we note especially the beauty of the Capitol grounds gardens and landscaping. And his attentiveness to the day-to-day wishes of his congressional employers cannot be doubted. But when it comes to supervising construction, Mr. White's record is--how shall we put it?--undistinguished.

Consider, for example, the architect's most recent production, the Hart Senate office building. The building ended up costing roughly three times as much as Mr. White's original estimate. It would have cost more if office paneling, rooftop restaurant and other planned features had not been eliminated. The final effect isn't bad if well-lighted mausoleums appeal to you.

Mr. White was a staunch proponent of the plan to "restore" the West Front by propping it up with a disfiguring extension--the better to provide high- tone hideaways for powerful congressmen. It took Congress almost 30 years to get up its courage to reject the extension plan--which had been justly opposed by the American Institute of Architects and a variety of historical preservation groups--and vote for true restoration instead. Having finally done so, it would seem only prudent for Congress to see that the restoration is supervised by someone who believes in it.

As Sen. D'Amato notes, however, his current amendment is a watered-down version of his initial --better--plan to place the restoration under the direct supervision of an independent architect. As it stands, the amendment would only require the appointment of a consulting architect to assist Mr. White. The senator was forced to this compromise by the opposition of Senate leaders who have still not endorsed the weakened amendment.

Come on, Senate--get this job going and get it going right; the result will be one the country has to live with.