Only the elect have a conscience?
What do you mean? Do you think our wants & desires come from a conscience?
By definition, only the elect have hearts that have been regenerated by God and minds that have been renewed by the Holy Spirit unto the truth of Christ risen.
"Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost" -- Titus 3:5