The worst reaction to any national government that embraced a car ban policy is the most predictable, punitive international financial measures prompted by the automotive industry bloc, one would hope that markets are not monolithic in this reaction and the novelty and insight into actual future conditions would also trigger new investment inflows.
Another reaction would be capital flight, if from local government this would need a state/provincial government ban to prevent subversion, a state ban would need national government ban. In theory a national ban would need an international one to cover it; but lacking global government flight from a nation should still reverse eventually due to global deterioration in oil supply and need for an operational urban workforce. It could yield a comparative advantage within decades as car based cities grow increasingly dysfunctional. Governments are not good at keeping such faith and one would expect vacillation from the ban policy; but the oil crisis really won't be that long in arriving.
Even if changing cities doesn't allow evasion of the ban because of overriding similitude of legislation, a geographic ban still leaves people free to relocate homes and businesses in country areas outside the ban area. Many elite bourgeoisies, who currently refer to anyone dependent on public transport as a "captive", would doubtless do this from ingrained perceptions and ideology. This is as it must be, some would be unable to reconcile to the new dispensation and this safety valve must be left open. Proscribed car city commuting would limit their environmental & resource impact, lower middle class emulation would be minimal as cheaper child-safe housing would be available in infill developments and their numbers would dwindle generationally from absence of the business and domestic benefits of urban living, which developed before the car age and would revive in its absence. Even the most car based landscape, the endless low density housing of California, would lose its gloss were car access to urban San Francisco and Los Angeles curtailed, and fashionable lifestyle options would trend toward infill developments.
However those who engage in this flight, possibly to car based microurbia, may be sufficiently numerous to pose the same problem for the metropolis as a whole as is posed currently to inner suburbs by the doughnut effect, city populations becoming disproportionately dominated by poorer, less rate paying people. Infill land sales, assets currently tied up by the car culture, would probably be required to prop up urban revenues for a decade or so. Any more aggressive reaction, mass drivethroughs or whatever, would need to have force met with force.(more 1)