Actually, this is a point of discontinuity with the novel, wherein Valjean's promise to Fantine was simply to bring Cosette back to live with her and provide means for their support (not to care for her himself), as he expected Fantine to recover from her illness. Thus, he asks Javert for three days simply to get said affairs in order, which Javert denies him.
In the ensuing scuffle, Fantine dies in the hospital, and Valjean is captured by Javert and is returned to prison. After some time, he finally escapes and only then does he go to meet the Thenardiers, now with the new intention of remaining hidden from the law and caring for Cosette as a father, believing that rectifying his failure to Fantine is more important than continuing to pay for a decades-old indiscretion.
That he asks for 3 days time in the confrontation lyric in my opinion, represents a challenging part in the conversion process from book to musical. Going through the entire capture, conviction, and prison escape of the novel would be too long and cumbersome, but if Valjean simply plans from the start to flee from the law, it would make the honor and conviction of "Who Am I?" seem trivial or dishonest.
Thus, we are left with this slightly clumsy spot in the adaptation. I think the intention was to present what others here have suggested- that Javert's denial of Valjean somehow voided Valjean's responsibility to the law, and readers of the book will recognize Valjean's honest intent to do what is right in God's sight. However, the way his plan changes is never fully reconciled in the narrative of the musical, which can be confusing for those unfamiliar with Hugo's original.