Marx didn't plan for lower prices.
Marx' theory starts with the same assumption as those arguing for basic income: That labour will eventually - as a natural effect of the drive of capitalism to compete - need to be automated away or squeezed on income, until capitalism faces the dual thread of causing mass unemployment (and so unrest) and too high manufacturing capacity (by driving incomes and employment down and so killing demand). This is outlined many places, but most prominently in the Communist Manifesto.
If that gets bad enough to lead to revolution, Marx "plan" was for a socialist government to use methods such as extremely progressive taxation and the like to basically drive capitalists into the working class. This is outlined in the Communist Manifesto and Critique of the Gotha Programme and many other places.
Once this leads to the end of class rule, Marx believed society would eventually take advantage of the overcapacity built by capitalism to allow distribution according to need. This is also covered in the Communist Manifesto, but expanded on at length in the Critique of the Gotha Programme.
Marx did make the assumption that class struggle will cease if everyone basic needs are met, but he also cautioned a number of places, and most notably in The German Ideology, that attempting redistribution in a society that was not sufficiently advanced to be able to meet the needs of everyone would just restart the class struggle all over again.
You may be right that the threshold for what people "need" before they will be satisfied may be higher than what Marx may have thought, but the point Marx made was not that people won't want more, but at some point peoples willingness to fight for a bigger share than what others get will be lower than such a society's willingness and ability to resist special treatment. Where exactly that point would be, we don't know.
The more immediately relevant question is whether Marx' prediction of capitalist boom and bust cycles eventually running out of control and driving unemployment so out of control as to trigger revolutions will prove correct.
Basic income would be a simple way of proving him wrong, by creating a safety net that would prevent things from getting bad enough to trigger revolutions.
Marx argument there is that the ruling classes will resist these types of redistribution, with violence if necessary, and that is the reason for the Marxist idea that revolutions are in general necessary - it comes not from any idea that they are desirable, but from an assumption that any working class majority for large scale redistribution will be faced with an army. If that proves wrong, then that pulls the rug under large parts of Marx' historical materialism (the idea that history is defined in part by the predominant modes of production, and that these inevitably evolve in certain ways culminating with the end of class rule).