With the government expected to exhaust its credit within a month, the Senate Finance Committee yesterday approved legislation requested by the Reagan administration to raise the national debt ceiling by $244 billion to $2.323 trillion.

Committee approval of the increase, expected to be sufficient to last through September 1987, came as debate continued over an anticipated amendment to overcome Supreme Court objections to the Gramm-Rudman-Hollings deficit-reduction law that was passed as part of last year's debt-ceiling bill.

The debt-ceiling increase, passed by the House as part of its fiscal 1987 budget resolution, was approved by the Senate committee, 10 to 2, with Sens. Charles E. Grassley (R-Iowa) and Steven D. Symms (R-Idaho) in dissent. The committee also approved, by voice vote, a provision to make it illegal for the Treasury to borrow operating funds from the Social Security trust funds.

"This generation has somehow accepted that it's morally okay to live beyond its income and beyond its means," said Grassley in objection to the debt-ceiling increase.

But the administration argued that Congress has no choice but to increase the debt ceiling and thereby extend the government's authority to borrow money if the country is to avoid financial default.

Without the increase, the Treasury Department said in testimony before the committee, the government would hit the current debt ceiling of $2.079 trillion by Aug. 1 and face financial default by Aug. 15, the day Congress is scheduled to begin a three-week recess.

"Default is an intolerable choice," said Assistant Treasury Secretary Charles O. Sethness in urging the Senate to follow the lead of the House by enacting the increase without controversy over amendments.

But controversy is likely in the form of an amendment from Sens. Phil Gramm (R-Tex.), Warren B. Rudman (R-N.H.) and Ernest F. Hollings (D-S.C.), principal sponsors of last year's deficit-reduction law, to revise automatic spending-cutback provisions that were invalidated last week by the Supreme Court.

The law called for the comptroller general, as head of the General Accounting Office, to be the final authority on spending cuts that are to be triggered if Congress fails to come within $10 billion of meeting annual deficit ceilings specified in the legislation. The target for next year is $144 billion, and both administration and congressional budget officials have indicated the deficit is likely to exceed $154 billion.

The Supreme Court objected to GAO's role on separation-of-powers grounds. Gramm, Rudman and Hollings have been exploring both a change in GAO to meet the court's objections and a transfer of authority for imposing the cuts to the administration's Office of Management and Budget (OMB), which appears to be legal under the court's guidelines.

The second of these potential solutions is under increasing discussion on the Hill. But Democrats in particular are balking at giving such power to the executive branch.

However, both Comptroller General Charles A. Bowsher and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) have objected to loosening the ties between the GAO and Congress. O'Neill has said that giving the budget-cutting power to OMB would be preferable to Congress' giving up control over the GAO.

Gramm and Rudman also indicated yesterday that they may opt for OMB as the solution but held off any decision in hopes of avoiding a dispute with the House Democrats. Rep. Leon E. Panetta (D-Calif.) said there is "real concern" in the House about both the GAO and the OMB alternatives, but added, "We don't know how to do it enforce Gramm-Rudman-Hollings otherwise.