The American people would likely to see dramatic changes to how politics are run in this country. According to Gallup, a large majority of Americans want shorter campaigns, a national presidential primary day and some form of national ballot initiative/referendum system. From Gallup:
Of the three changes, creating a shorter presidential election is probably practically impossible as long as we have a fixed election day. Even if we amend the constitution to make it possible to pass a law mandating a five week election, it would probably be impossible to stop groups from running “issue ads” and candidates from doing campaign like events ahead of time. We would have campaigns in all but name.
The other two changes could at least be implemented if there was the political will to change the law.
There is no logistical reason why the presidential primary in every state could not happen on the same day. It would simply require all the states to agree. Forcing states like Iowa or New Hampshire to give up their special spot though would require some real determination. If one of the major parties take a hard line refusing to seat any delegates not selected on the national primary date then it might work. There is also the option of Congress passing a law to pay the cost of running the primary but only on the one day, which might slowly encourage a shift.
A national ballot initiative and/or referendum system could work but would probably need a constitutional amendment. Half the states use it for state issues and some countries, like Switzerland, have a national referendum system. While people on all sides can argue the merits of the idea it easily could function.
It is unfortunate that Gallup didn’t provide a state level breakdown for this referendum question. I would love to see if people who live in states that already have an initiative/referendum process are more or less likely to want to see the idea adopted nationally.