Go here to read about the peace initiative of Francis P. Blair who travelled to Richmond to meet with President Davis.
Jefferson Davis was a very shrewd man, much shrewder I think than most historians have given him credit for being. He realized that little could be expected from negotiations with Lincoln because Lincoln would never agree to Confederate independence, the one non-negotiable issue as far as both Lincoln and Davis were concerned. Additionally, he regarded a joint Union Confederate war against the French in Mexico, the core of the Blair initiative, to be a fairly bizarre proposal. However, he was eager to negotiate. The Confederate military situation was beyond dire. If the negotiations led to Confederate independence, victory would be snatched at the last instant. If, as Davis expected, the negotiations led to nothing, he could tell his people that he had attempted negotiations and the Union would not negotiate in good faith, and all that remained was a last ditch struggle to secure on the battlefield what the North would never concede on the negotiating table. Here is the note that he gave to Blair to take back to Lincoln:
RICHMOND, VA., January 12, 1865.
F. P. BLAIR, Esq.:
SIR: I have deemed it proper, and probably desirable to you, to give you in this form the substance of remarks made by me, to be repeated by you to President Lincoln, &c.
I have no disposition to find obstacles in forms, and am willing, now as heretofore, to enter into negotiations for the restoration of peace; and am ready to send a commission, whenever I have reason to suppose it will be received, or to receive a commission, if the United States Government shall choose to send one. That notwithstanding the rejection of our former offers, I would, if you could promise that a commissioner, minister, or other agent would be received, appoint one immediately, and renew the effort to enter into conference, with a view to secure peace to the two countries.