I agree with evaoslik. There's no idiomatic single-word way of conveying
the „ještě“, and certainly not „right
today“. Normally the emphasis in „ještě dnes“
will be conveyed by the correct sentence stress and intonation, and by the
context, which will typically suggest something like „how
soon can you do it?“. „As early as today“ is possible, but doesn't sound
natural in conversation, where the sentence stress and intonation would normally
convey the emphasis.
One way of helping to reinforce the „immediacy“ of the completed action
(„udělat“) is to say „I'll get it
done today“ (instead of „I'll do it“).
I'll Do It Tomorrow: How to Stop Putting It Off and Get It Done Today (goodreads)
Another option:
„Povězte vašim dětem, co se stalo. Potřebujeme si s nimi promluvit.
Jejich výslech samozřejmě nespěchá. Určitě by ale bylo moudré udělat to
ještě dnes. Bude lepší, když to uslyší od vás než od někoho
jiného" – … but it would certainly be wise to do it no later than today / this very
day / before the day is out. It will be
better for them to hear it from you than from someone else. (Google
books)