Breadline as a term related to poverty is also familiar to Americans, but not in the phrase on the breadline.
The earliest attestation in the OED to the bread line representing an income level supporting only basic subsistence is actually from a U.S. source, a labor statistician named Matthew Simpelaar writing in 1888. This meaning, however, has been overwhelmingly supplanted by a contemporaneous definition, of a queue one stands in to receive free bread. Rather than living on the breadline or living below the breadline, people receiving free food from a charity are literally standing in breadlines (ironically, outside what are colloquially known as soup kitchens). The phrase is strongly associated with the Great Depression and the era's evocative photos of breadlines.
The minimum income level deemed adequate for basic living standards is most commonly called the poverty line, a colloquialism popularized during the expansion of welfare programs in the 1960s which were based on definitions developed by statistician Mollie Orshansky. Someone living at or on the poverty line is someone barely getting by; someone living below the poverty line is impoverished and cannot maintain an adequate standard of living. Few Americans outside of those in public policy could guess accurately as to what the Orshansky Poverty Thresholds actually are, but as they are increasingly criticized as out-of-date, that may be just as well.
More casual phrases one may encounter are living hand-to-mouth or living paycheck-to-paycheck. Both indicate a situation where one is barely (if at all) meeting current spending demands, without the ability to plan for the future, but hand-to-mouth carries an image of dire poverty—of being so hungry you devour a morsel of food as soon as it is handed to you—whereas the latter is much broader, and can be applied to middle-class or upper-class people who have a comfortable standard of living but are unable or unwilling to save money for emergencies.