DETROIT — General Motors Corporation is preparing to launch a public bond-exchange offer to wipe out most of its $28 billion unsecured debt by June 1 to avoid bankruptcy. President Barack Obama gave the company 60 more days to get the concessions it needs. GM spokeswoman Julie Gibson said “We have a large pool of people we need to reach, and the only way to do that is through a public offering.”

The company has thousands of bondholders who must soon decide whether to participate in an offer and ensure they get at least a small amount of their investment back, otherwise they will land up empty handed. To get more government aid the company will have to restructure by cutting few jobs and other costs, it should also get some concessions from its unions.

Gibson said it’s unclear whether the bondholders committee will have any say in the offer because GM was working with the bondholders committee to strike an exchange deal, but they rejected an offer that would have given them cash, new debt and equity.