Mas vale que cumplas

Mas vale que cumplas
 

Acabo de oír algo. Creo que la frase completa fue "Que hago responsable. Mas vale que cumplas." ¿Que significa "mas vale que cumplas?" ¿Lo oí correctamente?

It must be "Te hago responsable. Más vale que cumplas".

There are several ways to say that depending on the context:

"I make you responsible. You had better keep your promise"

or "you had better do your job"

or "you had better fulfill/achieve the objects"

or "you had better comply".

And several others, but I think you get the idea.

Lo de primero no es lo que dijeron.
La frase que quieres saber significa:
It's (more) important for you to accomplish/finish/fulfill (your promise, or whatever else they're talking about).
Depending on how it was used, it could also mean:
You had better do what you said you would.

Más vale que cumplas.

valer (present indicative, 3rd-person singular)
cumplir (subjunctive mood, 2nd-person singular)

I agree with the above.

Just for extra information, should you be interested ... related to the phrase "más vale que cumplas" is the shorter phrase "más te vale" (used in Spain; not sure about other Spanish-speaking countries).

Generally speaking, this phrase would mean "you had better" (like a sort of warning, "you had better, or else!").

For example,

Daughter: "I'll clean my room this weekend."
Mum: "You'd better, otherwise, you won't be going to the party."

Hija: "Limpiaré mi cuarto este fin de semana."
Mamá: "Más te vale, o si no, no irás a la fiesta."