The financially troubled Dart Drug Stores Inc.'s overcame a last-minute snag last night in its attempts to restructure the company's massive debt and announced it obtained enough support for its debt-exchange proposal.

The company had asked holders of its $160 million in high-interest bonds to swap them for Dart stock and new, lower yielding bonds in an effort to reduce the company's large interest payments.

Dart had said it needed 85 percent of the bonds to be exchanged if the restructuring was to be successful. Otherwise, Dart said it might have to seek protection from creditors under federal bankruptcy laws.

But as of 5 p.m. only 50 percent of the year-old bonds had been turned in for exchange. As a result, Dart late yesterday extended the deadline for its exchange offer to 11:59 p.m. in hopes of gaining more bonds. Early this morning, Dart announced it had completed the deal -- even though 82.5 percent of the bonds were exchanged, less than Dart had hoped for.

In repeated filings to the Securities and Exchange Commission, Dart has said, "If the exchange offer is not successfully consummated, the company may be forced to seek a reorganization under Chapter 11," of the bankruptcy laws. "Under certain circumstances, the company may be forced into liquidation under Chapter 7 of the bankruptcy code," Dart added.

On Thursday, when Dart announced that only 10.7 percent of the bonds had been tendered, sources close to Dart said the company remained confident that the exchange offer would succeed.

Wall Street officials also seemed confident, saying investors typically waited until the last minute to exchange securities, although some investors privately said the Dart exchange could be a close call.

If Dart failed to gain enough bonds, some investors predicted the company would try to sweeten its debt-exchange proposal to win sufficient support to make the restructuring work before the company resorts to bankruptcy proceedings.

Burdened by massive debt, Dart proposed its debt-exchange offer last April in an effort to cut its annual $28 million interest payments.

After several discussions with major bondholders, Dart improved its initial offer so that bondholders in the end were being asked to exchange each $1,000, 12.7 percent bond for a package of new securities worth about $766. The package consists of a $500 bond that will bear an initial 6 percent rate and increase by 1.1 percent semiannually as of 1990. Additionally, bondholders would get 24 shares of common stock, estimated to be worth about $3.50 a share, and 40 shares of preferred stock, each convertible into 1.3 shares of common stock.

If successful, the debt-exchange proposal was expected to cut in half the company's annual interest payments. The immediate result would be to make Dart profitable. With the company's huge debt load, its liabilities exceeded its assets by more than $32 million last year.

Dart's financial woes stem in large part from management's acquisition of the drugstore chain from Washington's Haft family in 1984 for $160 million. The Hafts wanted to spin off the chain that the senior Haft founded in the mid-'50s to concentrate on other retailing ventures.

Management agreed to buy the chain. But to finance the debt incurred from the acquisition, Dart last year issued $160 million in bonds. Coupled with a downturn in drugstore sales last summer and fall, Dart found it increasingly difficult to meet the semiannual interest payments.

Dart has already failed to make a $10.2 million interest payment on the $160 million bonds. But Dart said the bank had not officially declared the company in default.