I think you're confusing the timeline of events, Davis and Lee only became prominent figures in the South after the war had started. Davis did have some recognition and respect from the various state legislatures who named him president of the CSA, but not nearly enough to have stopped the secession process in its tracks. Lee was only a Colonel in the regular army and was far from public eye having spent a great deal of his time in Texas away from politicians and prominence that those connections would have afforded him. Even at the start of the war Lee was only truly well known and respected in his home state of Virginia.

Another problem is that while you are correct in the idea that both men were opposed to secession your confusing as to why they were opposed. Davis for his part believed that all states had the right to withdraw, but preached patience in his, rather correct, belief that the North wouldn't let them leave peacefully. He believed in the political process and didn't think secession held the answer because he didn't think the South had a good chance of besting the North in a war. Lee also believed the states had the right to secede, but like Davis was hopeful and confident in the political process itself. However, both men were also men of deep principal and loyalty to their home states, which they viewed as being within their rights to withdraw from the Union. When Mississippi left Davis referred to it as the "saddest day of his life" in his farewell speech to the Senate. Lee was also terribly saddened by Virginia's withdrawal, but both men saw it as their duty to aid and serve their states in whatever capacity they could.

Neither Davis nor Lee were in a position to greatly alter the outcome of various state legislatures during 1860-61. In fact I believe that only one man could have affected the outcome of the legislatures decisions and that man is Abraham Lincoln and the only way he could have changed their minds was to concede the election to a southern president like Breckenridge.

It is interesting to note here that Robert E Lee did not take full command of the Army of Northern Virginia when the war broke out. Many believe that he was actually offered command of the Federal Army but turned it down. It is known that he took command of the Virginia Militia and below is what he said to the assembly upon taking command.

"MR. PRESIDENT AND GENTLEMEN OF THE CONVENTION:—Profoundly impressed with the solemnity of the occasion, for which I must say I was not prepared, I accept the position assigned me by your partiality. I would have much preferred your choice had fallen upon an abler man. Trusting in Almighty God, an approving conscience, and the aid of my fellow-citizens, I devote myself to the service of my native State, in whose behalf alone will I ever again draw my sword."