That clause is NOT qualified by the language you cite. In other words, Congress CANNOT strip the court of jurisdiction over cases "in which a state shall be a party." Several states were parties to the ObamaCare lawsuit. As such, Congress had NO power (under the language of the "damn Constitution," as you put it) to strip the court of jurisdiction.
And, even where Congress can strip the courts of jurisdiction, it can only do so by passing a law. Article 1, Section 8 states that "The Congress shall have power . . ." That doesn't mean that Congress can do all of the things in Article 1, Section 8 without the President's signature.
Finally, again, stripping the courts of jurisdiction over the ObamaCare cases would not have accomplished anything. We WANTED judicial review of the law, because the law was passed by Congress. The case did not go as we wanted it to go, but it at least gave us a chance. Had the courts lacked jurisdiction to hear the cases, ObamaCare would have stood, no questions asked. How would stripping the courts of jurisdiction over ObamaCare have helped get rid of ObamaCare?
"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."