One of the women was a former Playboy model and the other an adult-film star.
Cohen said that he made the payments at the "direction" of a candidate for federal office. He did not name Donald Trump, but his lawyer did, accusing the President of directing Cohen to commit the crime of influencing the outcome of an election.
Trump had said previously he knew nothing about the payments.
These are turbulent and potentially perilous days for the President; in effect, he stands accused of conspiring to direct a crime but, even so, it is far from certain his approval ratings will collapse.
A fightback has started.
Cohen is referred to by the President as "the rat".
Some of his supporters are pointing to Cohen's "pattern of lies and dishonesty".
One talent that Trump has demonstrated time and again is that he understands the beating heart of his base, his core supporters.
Just before the 2016 election, a tape emerged of Trump boasting that he could do anything he wanted with women because he was famous.
His words "grab them by the p****" would have destroyed most candidacies and I remember there were fears inside his campaign that he had been fatally damaged.
Trump dismissed it as "locker-room talk", and he went on to win 62 per cent of the votes of white women without college education.
From the start of his presidency, Trump has assiduously nurtured his base by delivering on his campaign promises.
He frequently tweets about what he has achieved as if ticking off a list. He often adds the word "win" to his claims of promises delivered.
Taxes have been lowered; he has taken on China over trade; he has fought to bring back jobs to America; he may not have built the wall along the Mexican border but he has been a vocal opponent of immigration.
In 2016, he promised that the "forgotten people would be forgotten no more".
He tapped into their fear and resentment that they were not just being left behind but they were "deplorables" despised by the elites. His campaign slogan "Make America Great Again" drew on nostalgia for an older, different, less diverse America.
Evangelicals might not have liked lurid stories about Trump's private life, but they have been ready to forgive him if it meant nominating conservative judges to the Supreme Court or defending gun rights and delivering a fast-charging economy.
After Cohen's dramatic guilty plea, the President went to a rally in West Virginia.
There were no hostile interruptions, no boos. His supporters were as passionate as ever. To many Republican voters, he has done exactly what he promised and his unconventional presidency is a hallmark of his authenticity.
Judgment on his presidency will come in the Midterm elections in November.
If the Democrats seize control of the House of Representatives, some will push to start impeachment proceedings but others will be more cautious.
I remember how Bill Clinton's impeachment drained all the political energy from Washington.
He had declared "I did not have sexual relations with that woman" and was impeached for lying under oath by the House, although later acquitted by the Senate.
I recall how the country recoiled at the salacious details of his Oval Office encounters with Monica Lewinsky. Afterwards, Clinton's approval ratings were back where they started.
For the current president, there are two key questions.
What will the investigation by Robert Mueller into collusion with Russia unearth? And how will the Republican Party react to the current turmoil?
The party has become the party of Trump. The White House will be watching closely to see if senior Republicans begin distancing themselves from him.
One casualty of the Trump presidency has been truth.
Papers have called out his lies and misleading statements. Polls suggest voters struggle to know what is fake and what isn't.
There will be many Trump supporters who will see this latest crisis as just part of the conspiracy against him; that a "deep state" has been plotting to undermine his presidency.
At stake here is a wider concern. What happens if there is an attempt to impeach Trump while half of Americans continue to support him?
The Trump presidency is set to test America's democracy and institutions.
- Gavin Hewitt covered the Trump election campaign for the BBC
