Took a while to reply because I wanted to give a decent answer. I'm not old enough to have any firsthand knowledge of '68, but I've read a few things about the '68 election. I mean, 1968 was its own thing - RFK was assassinated, MLK was assassinated, segregation was just beginning to end. Many events that have no parallels today, just as the situation today has many aspects that have no parallels in 1968 - the internet in general and the economic situation being some I could name.
In 1968 you have like 3 television channels and maybe you read the newspaper. The rest of your information came from personal experiences which are colored by your location and social group. I think a lot more people back then took their information from single, mass channels and it caused a majority to have unified opinions about national policy. This is... not the case today. I don't think I need to really write a huge amount explaining the internet's impact on socialization, but in the context of America it had the effect of breaking down the information gap that comes about as a result of the physical isolation of America from other continents. We're connected to people we would never have met before, and we can glimpse the full variety of opinions about issues at a glance. On the negative side, it becomes easier to manipulate information (by third parties; maybe not by states) and fradulently push political narratives. To put it simply, the establishment had better control of what Americans knew about the world, the war, the protests, etc in 1968. A lot of people of course didn't buy the general narrative of the media in 1968, but in 2020 the mass narrative is much, much weaker and is in constant competition with many others.
In 1968 the United States was absolutely dominating economically. GDP is a stupid measure, but I'm too lazy to make this comprehensive, so I'll mention that US GDP at the time was about equal to all of Europe plus the Soviet Union (getting numbers on Soviet GDP is hard so this sum may be bullshit, but regardless, America was really fucking economically powerful at the time). This wealth was also distributed more evenly than it was today (the US has always been an oligarchy, but it's gotten much worse since then.) That means the average (white) person was making money, might have had a house paid off, etc; they were doing well. I've read a huge amount about life in 1968 and almost nowhere does anyone mention being worried about making rent or getting a job or paying off student loans or medical bills. The poor are always out there, but Americans could pretty easily look at their lifestyles and know that they were better off than any country on earth. What is there to protest about? Just beat communism and we won't have to send people to die in jungles anymore, then we can all drive cars around, high five, and say "america number one" while having it actually be true. It seemed obvious that American capitalism was providing the goods, so may as well stay the course, right?
Today, the US is in a very, very different position. There is no Cold War, and no equivalent (China is not equivalent. I just bought like ten things from there. Americans were not buying products made in the USSR in 1968, they were thinking about whether or not to nuke them). This is a multipolar world. And with the Internet, it's easier to look at other countries and say "Hey, shit, I wish we had that. Why don't we have that? That looks like a better life." I sure as hell look at the NHS that way. Lots and lots and lots of Americans do now. I remember reading a discussion online where a European didn't know what a "deductible" was, and I wished I didn't know what it was. Seeing other countries with better functioning democracies, better healthcare, equal or more effective industry, affordable housing, etc, you realize that there's political improvements to be made. Some idiots will close their eyes and cram their fingers in their ears and yell "lalala America is the best place to live in the world, everyone wishes they were Americans", or they ignore any mention of a foreign country with a better way and call it "america bashing", and some people are just old and used to USA = #1 and refuse to believe otherwise. But Americans are really starting to notice that their lives could be better because there are other countries that seem to be doing better, and you can watch a video on your phone if you want proof.
What's kind of interesting to me is that "economic memory" seems to be very weak in America, it's still not widely understood just how cheap college and housing were 40-50 years ago and what that meant for poorer people's quality of life. My life would be very, very different if renting an apartment was like $80 a month. When I realized this gap in housing costs for the first time, it changed my whole view of the '60s in America. It would have been fucking easy to smoke weed and read political theory and go out to protests and just pick up a job whereever on occasion and get enough money to travel around for months back then. And if you did work and save for a few years you could own a house outright. That was genuinely possible back then, and it isn't now for most. Those who did come of age in the '60s sometimes still believe that this is easily achievable, but it really isn't for most professions and areas. You can't get a job that will pay off a house in a few years unless you have a postgraduate degree; even then you've got a tough road. Americans my age have been working like crazy to survive for years. Nobody I know owns a house, though I know people who got mortgages, then lost their jobs and had to short sell, leaving them in debt. In 1968 they had just passed LBJ's great society programs, which included rent subsidies, medicaid and medicare, and they all applied FAR more broadly to the population than the extremely restrictive social assistance programs the US has today. All that stuff you have to pay for now, and it's eaten away at the financially stable silent majority sorts.
Electorally, Trump doesn't have and has never had a "silent majority", he has only ever had a hardcore minority of support and votes in the right places to make it into the white house despite losing the popular vote by three million. He has a majority in more rural areas but they aren't silent in the least. Though I do see that the popular vote was close in '68, Nixon won that by ~500,000 votes. I would imagine at a personal level Nixon was much more respected than Trump, because I think he could probably speak coherent sentences and not pointlessly antagonize people at every opportunity. These are all just some of the differences that would lead to there really not being a similar "silent majority" today.