Nope, Art III, Sec 2, Para 2 says:
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.
Paragraph 1 provides the full list:
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority;--to all Cases affecting Ambassadors, other public Ministers and Consuls;--to all Cases of admiralty and maritime Jurisdiction;--to Controversies to which the United States shall be a Party;--to Controversies between two or more States;-- between a State and Citizens of another State,--between Citizens of different States,--between Citizens of the same State claiming Lands under Grants of different States, and between a State, or the Citizens thereof, and foreign States, Citizens or Subjects.
As you can see, cases arising under the Constitution are not in the Original Jurisdiction list of P2 and therefore are subject to the underlined provision: meaning that Congress can prohibit the USSC from hearing cases on, say, abortion.
Okay, I see what you’re saying. Cases concerning ambassadors and such and ones which states are a party to are the only kinds Congress can’t touch. But there’s another way around this. Some people think, and I tend to agree, that due process requires judicial review.