The phrase "without a minute spare" implies being pressed for time or having no free time available. There are numerous synonyms for this phrase such as overburdened, swamped, squeezed, loaded, or inundated. These terms convey a sense of being overloaded with work or responsibilities, leaving no time for leisure or relaxation. Other synonyms include "engaged," "occupied," and "preoccupied," suggesting that one's attention is fully absorbed in a particular task, leaving no room for other activities. Regardless of the specific synonym used, the meaning remains the same - a lack of free time to spare.