Meaning
Can't handle it / can't manage
Example
Não dou conta de tanto trabalho ao mesmo tempo.
I can't handle so much work at once.
Origin
This is a transparent, literal phrase rather than a colourful idiom. Dar conta de means "to account for" or "to be equal to" a task — to handle it successfully. Negated as não dar conta, it simply says you cannot manage or keep up, that the job is beyond you.
Practice idioms with the Idiom Trainer
Falando's Idiom Trainer teaches you to recognize idiom meanings and create sentences using them, so you can speak like a Brazilian.
More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity