Does grace nullify obligation for Christians?

Scripture tells us we are saved by grace. Our salvation is a free gift we cannot earn or boast about. All we need to do is sincerely place our faith in Jesus and we are saved. And since it is a gift, it is often described as being unconditional, no strings attached. But other Scriptures speak of a continuing responsibility, obligation, to remain in the faith. Which is it? Do Christians have a true obligation after sincerely accepting Jesus? Or do we have an iron-clad guarantee that once we have embraced Jesus, we will enter heaven, no matter what? How can we reconcile what appears to be an incongruity in Scripture?