2 years means 365 x 2 = 730 days.
When the IRS means "the end of the second calendar year" they say so. Not in this case.
Note that even if the widowed spouse waits more than 2 years, they have a stepped up basis on at least part of the house, that will reduce their capital gains even if they miss the exclusion window. Basis is discussed in publication 523, including certain adjustments to basis that will reduce the taxable gain, even if the exclusion is available.
https://www.irs.gov/forms-pubs/about-publication-523
