WASHINGTON — The head of the Treasury and the Federal Reserve began discussions on Thursday with Congressional leaders on what could become the biggest bailout in United States history.

While details remain to be worked out, the plan is likely to authorize the government to buy distressed mortgages at deep discounts from banks and other institutions. The proposal could result in the most direct commitment of taxpayer funds so far in the financial crisis that Fed and Treasury officials say is the worst they have ever seen.

Senior aides and lawmakers said the goal was to complete the legislation by the end of next week, when Congress is scheduled to adjourn. The legislation would grant new authority to the administration and require what several officials said would be a substantial appropriation of federal dollars, though no figures were disclosed in the meeting.

Democrats, having their own desire for a second round of economic aid for struggling Americans, see the administration’s request as a way to win White House approval of new spending to help stimulate the economy in exchange for support for the Treasury request. Democrats also say they will push for relief for homeowners faced with foreclosure in return for supporting any broad bailout of struggling financial institutions.