As far as I know, Davis was headed to Texas, not Mexico, but I could be wrong. I think some on the Western front held out hope of continuing the fight as long as Davis remained free. From Confederate Major General J. Bankhead Magruder to his Texas troops on May 10, 1865 [published in The Galveston Daily News, May 12, 1865; bold font is mine]:
Soldiers! Once more I say, let us be united, determined and defiant. Our President is doubtless on his way to the Trans-Mississippi Department. The Flag of the Confederacy will be kept proudly flying. Brave men, from every Confederate State, will rally to its support and swell your ranks.
The enemy cannot send half his force against you in the Trans-Mississippi Department, and whilst you are giving him a warm reception, opposing him at every step, your brethren beyond the Mississippi will again rise in their might and wage a battle, which will force the enemies' troops from this Department, to recover the territory which he occupied but had never conquered.
...the war will be renewed with greater vigor than ever, upon the soil of Virginia, South Carolina and their sister States, made sacred by the blood of a hundred thousand brave men...