Did the White Russian's really have a chance against them, or was it basically over and had a snowball's chance in hell?
Yes and no.
As early as late 1918, when the Bolshevik Party state apparatus was still busy establishing itself in Petrograd and Moscow proper (two cities rife with right-wing dissent in the early days of the civil war), a coup was highly possible.
The British naval commander Francis Cromie comes to mind as an individual who, had he lived,
might have been able to pull off a coup with broad support from officers, nobles, and middle class citizens.
But the Cheka nipped his little coup threat right in the bud rather quickly and efficiently. As harsh as the Cheka was, without a political police given unusual extraordinary powers to combat any and all threats to Bolshevism, the workers' and peasants' government of Lenin and Trotsky would have collapsed from within by internal dissent rather than from without by military might on the battlefield.
A right-wing, hugely conservative military regime would be in order, presupposing disbandment of the Red Guard workers' militia and the forcible dissolution of the soviets along with the obvious banning of the Bolshevik Party or any radical leftist force in general for that matter.
As for reasons why the Whites lost:
Popular support, the had none. The Reds had just a little, but just a little is way better than none.
This. As brutal as both sides were to the population as a whole, the Bolshevik vision of universal class struggle wrapped around the promise of workers' control of industry, revolutionary land reform, and direct soviet democracy attracted many more individuals over to the side of the Reds than the Whites were capable of attracting.
The Whites were mainly in opposition to the seizure of power by the radical (Bolshevik) left. However, no clear cut cause actually existed for what one would do after Bolshevism was vanquished. Some wanted a strong military dictatorship; others wanted the complete restoration of the Czarist monarchy; yet more yearned for the reconvening of a Constituent Assembly as to form a government firmly under moderate socialist control.
Rather than there being a single, unifying vision, there was a whole host of visions competing against each other struggling to assume mastery over the White movement.
Furthermore, for much of the civil war in a typical village, land reform was reversed in favor of the overthrown landowner, the local administrative soviet representing most of the village's populace was dissolved, etc.
It wasn't until 1921, in the Crimea under the White officer Wrangel, that the White movement finally figured out that it badly needed the support of the peasantry if it was to sustain an army in the field and ensure victory on the battlefield over the Reds
By that point, the White movement was all but dead. Wrangel's evacuation of his troops from the Crimea effectively ended any and all talk of a White Russian movement capable of resisting Bolshevism on its own without foreign support.
The Reds it can be argued won due to having persuaded the poor and middle peasants of the righteousness of their cause, which the average villager believed to be equated with land to the tiller which was enough of a promise for them to fall in closely behind the Bolsheviks' ranks.
The White Generals need less of an ego, too much useless soloing, too little coordinated efforts.
Indeed. They not only needed more sincere coordination between individual commanders out in the field, but they also desperately needed to rally around a sympathetic, commanding figure to rival Lenin's own charismatic stature and great statesmanship.
Hence the murder of Czar Nicholas II by the Cheka, as it was feared that the Whites could use him as a figure head for the rest of the nation to rally behind.
Kerensky, fully discredited and in exile, would hardly serve as a forceful leader capable of taking charge of millions. Besides, he himself had little interest in taking sides in the ensuing conflict regardless of whether or not a White officer or two asked him to head their cause.
For these reasons and many more, the Whites lost and the Reds won.