People usually say "live for the moment" Examples: He's a real party animal, he just lives for the moment. She never saves her money, she just lives for the moment.

the moment = 此时此刻 It literally means: Live in the moment. Focus your whole mind on the moment 此时此刻.

"Live in the moment" means to concentrate on the present, with little or no regard to the past and especially not the future. "Mozart died in poverty because he never saved any money for the future. He just lived in the moment." Sometimes you may hear it as "live for the moment". My Chinese is basic, but I think 得过且过 translates more to "marking time", which has a more negative flavor. 过一天算一天" is "living day-to-day" which is closer to the original meaning - however "living day-to-day" can also mean normal and mundane.