The Senate has dodged a U.S. debt disaster by approving legislation to lift the federal limit on new borrowing by nearly a half-trillion dollars.

Republican and Democratic senators have edged back from a perilous standoff over lifting the nation’s borrowing cap.

Senate Democrats signaled that they will accept Minority Leader Mitch McConnell's (R., Ky.) offer for a short-term extension of the debt limit, multiple senators told rep...