Socialism was not flourishing in the 40's, the 1830's and 1840's were the time period that Socialism as an ideology was coming into existence and was not a coheseive ideology that the masses would adopt.
Now, as to the idea itself, the Constitution can't be more 'liberal' or 'democratic' than it was, afterall the Constitution itself was essentially a compromise betwee the 13 colonies whom all had different ideas, and even if you could, what kinds of changes are you even meaning, I mean you could maybe get an electoral college that uses proportional voting, but you are'nt going to get a directly elected president, and you're certainly not going to be able to ban slavery.
Furthermore the 1840's are hardly a time period in which their was any great wanting of revolutionary change.
There would be as little difference from OTL as possible really. It mostly has to do with government actually representing the people's interests and local superiority over federal superiority. Maybe more of an emphasis on Jefferson's idea of revolution every 20 or so years. Anyway suffrage could be more egalitarian. Only small changes but they have great potential later and when they are repealed it has severe consequences.