The reference given is a bit vague.
There is an organisation at the University of Washington called the IHME
The Institute for Health Metrics and Evaluation (IHME) is an independent population health research center at UW Medicine, part of the University of Washington, that provides rigorous and comparable measurement of the world's most important health problems and evaluates the strategies used to address them.
Given they are health analysts from the University of Washington and they model the COVID-19 pandemic and produce projections, I am making the jump that this is to whom the New York Times video is referring.
Their current predictions for COVID-19 deaths in Mexico by August 4 are far more optimistic than 45,000.
The project 6859 deaths, with a 95% uncertainty interval ranging from 3,578 - 16,795. It predicts until August 4, not the end of (Northern Hemisphere) Summer.
This projection was made in May 29, 2020. (The video was published June 5, 2020.)
This answer does NOT attempt to show that:
- There wasn't another health analyst at UW that made the bigger prediction.
- That the model that the UW prediction is based on is "good", or that it is more accurate than a model that predicts the 45,000 estimate. [Update! See below]
It is intended to suggest that the New York Times reported prediction isn't in line with IHME modelling.
That said, the IHME projection seems to far too optimistic when compared with later data:
The ncov19.live dashboard puts Mexico's COVID-19 deaths at 12,545 (Hat tip to @DanielRHicks.) The John Hopkins Coronavirus resource center agree.
The best graph I could find to correspond with the prediction was from Wikipedia:
It shows that by May 21, the actual deaths were outside the May 29 projections!
I currently have no explanation for this discrepancy. It makes this answer far muddier.