Shortly before the media start-up The Messenger launched last year, its president said that the company planned to generate more than $100 million of revenue in 2024. It will need a major turn in fortune to get there, the New York Times reported. The site generated about $3 million in revenue last year, according to two people with knowledge of the company’s financial results. And it has told potential investors that it had only $1.8 million in cash on hand at the end of December, after losing about $38 million last year, putting it under severe financial strain. The operating results of The Messenger — which until now had not been fully disclosed — underscore the difficulties facing the company. The founders, who raised $50 million to start the website, initially said their aim was to transform coverage of U.S. politics, culture and sports. But it has run into editorial and financial troubles. This week the company is laying off roughly two dozen employees, including those who covered national politics, science and technology. It is raising money from investors to maintain its operations through this year. On Tuesday, Richard Beckman, a founder who was a long-serving executive at the magazine company Condé Nast, announced he was leaving the company.