fazer frente a / lutar / opor-se / enfrentar / ganhar / vencer / persuadir / convencer

carry the day
1. to win a war or a fight
Example: At the beginning of the American Civil War, many southerners believed their soldiers and statesmen would carry the day.
2. if you carry the day, you persuade people to support your ideas or opinions, or if a particular idea carries the day, it is accepted by a group of people
Examples: The Republicans carried the day in the dispute over the new jet fighter.
Her argument in favour of pay increases eventually carried the day.

from Cambridge International Dictionary of Idioms
http://dictionary.cambridge.org/