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
A literal phrase: dar conta de = 'to account for / to be equal to a task.' The negative is plain Portuguese for 'can't manage' and has no idiomatic origin beyond its straightforward sense.
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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