If indeed the headline is correct: Trump revokes waiver for California to set higher auto emissions standards, the waiver grants California the authority to set higher standards in favor of the environment. That being said, is there anything in law. that prevents California from setting the bar higher in the absence of said waiver?
Various US Federal laws, including the Clean Air act, identify air pollution as a matter of interstate commerce, and assert exclusive Federal control over it, except as specifically permitted by those laws.
The Clean Air act specifically provides for the California exception to set higher standards, and for other states to follow the CA rules if they so choose. What is not clear, at least to me, is whether the law permits the President to cancel the CA waiver at will. But in the absence of such a waiver, I believe that no state may set different standards on auto or other emissions from the Federal standards. This is to avoid having many different state standards, and to facilitate a national market, which is something Congress is empowered to promote in this way.
Of course, nothing prevents automakers from choosing to adhere to stricter standards than any law requires. They could even advertise "Buy X, the cleanest, greenest cars on the market". Whether this would pay I don't know.
I gather that various states intend to sue, claiming that the action is unlawful. I am not clear what legal arguments they will advance for this.
42 USC §7543 (aka Clean Air Act section 209) provides:
§7543. State standards
No State or any political subdivision thereof shall adopt or attempt to enforce any standard relating to the control of emissions from new motor vehicles or new motor vehicle engines subject to this part. No State shall require certification, inspection, or any other approval relating to the control of emissions from any new motor vehicle or new motor vehicle engine as condition precedent to the initial retail sale, titling (if any), or registration of such motor vehicle, motor vehicle engine, or equipment.
(1) The Administrator shall, after notice and opportunity for public hearing, waive application of this section to any State which has adopted standards (other than crankcase emission standards) for the control of emissions from new motor vehicles or new motor vehicle engines prior to March 30, 1966, if the State determines that the State standards will be, in the aggregate, at least as protective of public health and welfare as applicable Federal standards. No such waiver shall be granted if the Administrator finds that—
(A) the determination of the State is arbitrary and capricious,
(B) such State does not need such State standards to meet compelling and extraordinary conditions, or
(C) such State standards and accompanying enforcement procedures are not consistent with section 7521(a) of this title.
(2) If each State standard is at least as stringent as the comparable applicable Federal standard, such State standard shall be deemed to be at least as protective of health and welfare as such Federal standards for purposes of paragraph (1).
(3) In the case of any new motor vehicle or new motor vehicle engine to which State standards apply pursuant to a waiver granted under paragraph (1), compliance with such State standards shall be treated as compliance with applicable Federal standards for purposes of this subchapter.
The word "shall" near the start of 42 USC 7543 (b) (1) seems to require the issuance of a waiver whenever: a) a state adopted standards prior to March 30, 1966, b) the state standards are at least as strict as the federal standards, c) the state standards are not arbitrary and capricious d) the state needs the standards, and e) the state standards are consistent with section 7521(a). a) and b) clearly apply to the CA standards. I don't know if an argument can be sustained on any of the other issues, nor exactly what grounds the current administration has advanced for canceling the waiver.