All supreme elected officials within one jurisdiction should have veto powers. In other words, Presidents (the country’s supreme elected official), governors (the state’s supreme elected official), majors (the city’s supreme elected official), etc., should all have veto powers.
All elected officials that have veto powers should also have the line-item veto. However, a line-item veto should only require, at most, a simple majority to override. In some cases, perhaps for minor or relatively minor issues, as few as 40% or even 1/3 of the governing body would be required to successfully override a line-item veto.