We really have no idea what Mr. President and other Democrats are proposing, but from what I can discern, they seem to think that any time the government increases the tax rate that applies to a certain income bracket, the government will collect more tax revenue from those who fall in to that bracket.
This is idiotic for many reasons, but some people are convinced by that higher tax rates equate higher tax revenues.
I am going to guess that these would be the same sort of people who think a business would always make more money by charging more for the products it sells.
In my experience, no amount of logical argument convinces these people, but then, there are those who know some economics, but are not confident enough in their understanding. First, note the following fact and file it away: Total tax revenues as share of GDP have remained relatively flat in the post World War II era as shown in the following graph, prepared by the American Thinker:
Of course, if people were robots who kept doing the same thing regardless of tax rates, Mr. President would have a point. Higher tax rates would result in higher revenue for the government. But, that isn't so: People respond to incentives, i.e. rewards and penalties. The reward of work is not work itself: It is the money you earn by giving up the time during which you could be doing other things. Of course, money, in and of itself is worthless (this includes gold as well). The money you get to keep after you earn it by working determines the kinds of things you can do with the time left over from exchanging your time with someone else for money.
The government, in essence, is an authority that sells you a work permit: You get to work and make money, so long as you pay the price of making money to the government. We call that price "taxes," but they are essentially a price you pay to be able to earn the resources to do things you like with your free time.
In that sense, the government in a well functioning economy has a monopoly over the right to make money: You cannot make money without paying the price to the one authority that can forcibly take it from you.
Of course, the higher the price you have to pay to be able to make money, the lower the reward to working. After all, by working, you are taking time away from things that are more fun and enjoyable (otherwise, you would not have to be compensated for work ;-)
As a monopolist, the government faces a downward sloping demand curve for the "work permits": The higher the price, the fewer permits are sold. Whether this causes less tax revenue depends on how sensitive people are to the price of work.
Mr. President and his people seem to think people are not sensitive to tax rates at all: That is, they think incomes will remain the same, no matter what games government plays with tax rates.
In a world with multiple safety nets, however, people would be expected to even more sensitive to price of work: After all, you can still guarantee the benefits of money without having to exert effort to make it.
What is the alternative?
The alternative is to stop worrying about "the rich" and concentrate instead on policy that give the incentive to everyone to produce more. After all, even if rates do not change, if people produce more, there will be more tax revenues.
Simplifying the tax code, eliminating multiple brackets, exclusions, inclusions, deductions, exemptions, credits etc and settling on a competitive flat rate would lead people to focus not on trying to figure out the tax code to keep more of their money to actually producing stuff that people want.
Removing inflationary expectations by committing to reduced government spending would lengthen people's planning horizons and spur optimism, rather than the current rational expectation that whatever measly sum you can make will get wiped out by higher taxes or higher inflation or both.