There will be no amendment to ratify though without 3/4ths majority of the house and the senate – easily accointing for a majority of the US population – or a constitutional convention, also something not at all likely to occur without not just popular support but long standing grievances of the populace with the federal government.
The constitutional convention requires 2/3 of the state legislatures to approve it to convene, so popular support is no more relevant to it than it is to ratification. If you have enough legislatures willing to ratify some amendment, the same legislatures can also submit it for ratification.
I'm aware, I don't believe that the populations of any combination of 2/3rds of the states constitute a minority, and it's safe to assume that significant populations from the 1/3rd of stares would support whatever measure a convention was attempting to address whatever problem.
