This has been fact-checked extensively:
All following quotes are from the Washington Post.
It may be a stunning picture, but it’s also a highly misleading and cherry-picked one.
The most crucial thing to note at the outset is that just because someone died after getting the vaccine doesn’t mean they died because of it.
So when Tucker Carlson says "a total of 3,362 people apparently died after getting the COVID vaccines in the United States" that can include people who died in a car crash, or who already had a terminal illness. He quotes no figures for "people who died because of the Covid vaccine." The statistics he is quoting are entirely irrelevant to the safety of the Covid vaccine.
The data is unreliable.
[...]data in the VAERS system is unverified. Anyone can submit claims about what happened to them or someone they know. The idea is to give the Centers for Disease Control and Prevention tons of data to use and then evaluate potential links between vaccines and side effects. As The Washington Post’s Valerie Strauss noted last month:"anti-vaccination activists routinely exaggerate the dangers of vaccines by misinterpreting and misusing data from EudraVigilance and from the Vaccine Adverse Event Reporting System (VAERS), a U.S. government database that allows anyone to self-report “possible side effects or health problems” experienced after a vaccine, even minor ones such as soreness at the injection site."
In other words, the VAERS system contains any event that somebody, somewhere, with or without any medical or statistical training, with or without their own agenda, has reported as possibly being related to the Covid vaccines. It is intended as raw data that needs to be analysed, and the CDC has in fact done the analysis:
The CDC, for its part, says it has analyzed the reports of deaths after coronavirus vaccines through May 3 and found no connection between the vaccine and deaths. “A review of available clinical information, including death certificates, autopsy, and medical records has not established a causal link to COVID-19 vaccines,” it says.
The flu figures are much more restrictive, and only contain deaths if they occur after one of a specific list of adverse effects that occurs in a relatively short time window.
The figures Carlson quotes for Covid and flu vaccines are in no way comparable.
Even without this counter-information, 30 people dying per day is not alarming.
According to CDC data, an estimated 8,000 Americans die every day of all causes. That’s 1 in every 41,000 people, every day. If you apply that number to 135 million people who are vaccinated, you’d expect that more than 3,000 people who were vaccinated would be dying every day right now — again, of something. That’s significantly more than the 30 per day Carlson suggests is alarming.
We expect about 8000 people a day to die in the US, and with 135 million vaccinated we expect about 3300 people with the vaccine to die each day - almost all of things entirely unrelated to the vaccine, but still (as Carlson puts it) "after getting the vaccine". (8000*135/328=3292). So having 3000 people with the vaccine die in a few months is not in the slightest unexpected.
And the vaccinated population isn’t just a random sample of 135 million Americans; the earliest vaccine efforts focused on elderly people who were more susceptible to the worst of the virus — and were also more susceptible to dying of other causes. In other words, we’d expect more deaths from all causes of vaccinated people.
The figures for people dying after the flu vaccine are wrong.
There is no question that exponentially more than 203 out of 100 million people who got the flu vaccine in 2019 went on to die of something in the months that followed.
Specifically about 2000 people (3000 * 100/135, or 8000 * 100/328) are expected to die every day after they get the flu shot (virtually all for entirely unrelated reasons), which is hugely different from the figure of 203 per year that Carlson quotes. Carlson actually flips between saying his numbers are "after getting the flu shot" and "from the flu shot", another reason to not take his piece seriously. In any case, he is quoting two completely different measures for flu and Covid, and is being misleading by trying to compare the two.
Also please read Fizz's answer which explains why the reporting of deaths for Covid and flu vaccines are so different.