I don’t think the Supremes have ever just flat out made up a right out of whole cloth, with no reference to any Constitutional provision. (I mean, various opponents of this or that political idea have accused them of doing that, but the Court has always had at least some theoretical Constitutional justification for its actions.) For instance, the “right to privacy” was found, IIRC, in the “penumbras” of various other explicit Constitutional provisions.
So, just whacking the First Amendment might not be enough to do away with a right–there’s also the Ninth and Tenth Amendments and the Fourteenth Amendment and so on. But, if you went through and systematically whacked every clause or amendment which contributed to the “penumbras” surrounding a right, there wouldn’t be anything the Court could do, except maybe resign en masse. Theoretically, you could declare the Church of Bucknerism to be the state religion and mandate that all heretics from orthodox Bucknerism be burned at the stake, and if you were sufficiently thorough with your amendments in expunging the Constitution of un-Bucknerist ideas and you could get two-thirds of both houses of Congress and three-fourths of the state legislatures (or three-fourths of the ratifying conventions called in each state, if that’s how Congress specified the amendment be considered) to buy it, the Supreme Court couldn’t do jack. For that matter, I suspect that an amendment which simply stated “anything else in this Constitution to the contrary notwithstanding” would settle the matter, whatever the matter might be. Also, an amendment which simply stated “there is no right to privacy” (or, more realistically, which outlawed abortion) would trump any “penumbras” or court decisions or precedents.
Conceivably, if the framers of the amendment got too cute with the wording, an unsympathetic court might wiggle out of it and send them back to the drawing board–if you said “abortion shall be illegal”, that’s kind of hard to ignore; if you said “all laws of the United States must respect the sanctity of human life”, that might still be open to interpretation. I think most proposed anti-abortion amendments talk about human life beginning at conception, and maybe even guarantee equal rights to the unborn, without actually using the words “abortion is henceforth against the law”. That would probably still be pretty hard for a pro-choice court to wiggle out of.
Remember, we’re talking about the U.S. Constitution, not a state constitution. This is especially important as I suspect the Colorado Supremes did in that amendment because they held it violated provisions of the U.S. Constitution. The U.S. Constitution is the “supreme law of the land” and trumps any state constitution if the two conflict.