This notion typically stems from a misunderstanding of our progressive income tax. The bracket rate only applies to the taxable income within that bracket, so if you earn more, only the extra money is taxed at the higher rate. If an individual had taxable income of $9,625, they'd pay 10% on the first $9,525 and 12% on $100. If they had $82,600 in taxable income, they'd pay 10% on the first $9,525, 12% on the next $29,175, 22% on the next $43,800, and 24% on the last $100.
Rate Individuals
10% Up to $9,525
12% $9,526 to $38,700
22% $38,701 to $82,500
24% $82,501 to $157,500
32% $157,501 to $200,000
35% $200,001 to $500,000
37% over $500,000
So, in general, no, increased income is not entirely offset by increased taxes. There are edge cases where increased income would mean you no longer qualify for certain programs/benefits that could result in a decrease your net income. Many deductions have phase outs to avoid creating cliffs, but I'm pretty confident some still exist, hopefully someone else knows of some examples offhand.