[What you need to know to start the day: Get New York Today in your inbox.]

The first phase of what was to be a sweeping plan to provide half-priced subway and bus rides to the poorest New Yorkers arrived on Friday, a few days late and many people short.

If the plan had been presented last year as a major change in the lives of those struggling to make ends meet in New York City, the reality, announced by Mayor Bill de Blasio and Corey Johnson, the City Council speaker, is far less than anticipated: Only 30,000 New Yorkers — those who already receive cash assistance from the city and are employed — will be eligible for the cards starting this month.

The pool of eligible New Yorkers would expand in April to about 130,000 people who receive federal food stamps and are working, Mr. de Blasio and Mr. Johnson said — still a far cry from the 800,000 New Yorkers estimated by advocates to live below the federal poverty line of $25,000 a year for a family of four.

The city has no mechanism for people to apply for the discounts; only those who receive cash benefits or food stamps can get the half-priced MetroCards.