No. The Social Security Administration is not a budgetary committee. The Social Security Administration denies benefits based on whether they believe that the applicant has a legitimate and pressing need to receive those benefits. If they don’t believe as much, the benefits are denied.
More often than not, you’re going to have to appeal your claim. More than half are denied in the initial stage and almost all are denied on reconsideration. This does not, however, have to do with the Social Security Administration factoring in government debt into their decisions.