Chances are that Congress will raise the federal debt ceiling before the country runs out of money to pay its bills. But up until the point Congress actually acts, fixed-income investors could find playing the odds harder and harder to do.

The Treasury Department has said it has until Oct. 17 before it exhausts emergency measures to avoid falling behind on its obligations. At that point, it says it will have $30 billion on hand—enough to cover its needs for another two weeks or so, estimates Wrightson ICAP economist Lou...