If I fail to notify the landlord 60 days before the end date of my lease and there are no stated consequences, am I obligated to pay rent after it ends?

If you don't give notice and your lease ends, the landlord can either evict you or treat you as a holdover tenant subject to a month to month lease.  If the landlord accepts a rent payment from you, the landlord is then treating you as a month to month tenant.  A month to month tenancy requires thirty days written notice to terminate.

Another possibility is if you move out without giving your current required sixty days notice, you will remain liable for the rent until the place is re-rented.  When the place is re-rented, your obligation to pay rent ends.  The landlord cannot allow the place to remain vacant without making reasonable efforts to find another tenant.  If the landlord allows the place to remain vacant without making reasonable efforts to find another tenant, the landlord will have failed to mitigate (minimize) damages (the amount the landlord is claiming you owe) and the landlord's damages will be reduced accordingly.  Reasonable efforts by the landlord to find another tenant will be determined by what other landlords in the area are doing to attract tenants; for example, posting a sign on the premises advertising the vacancy, advertising the vacancy in the newspaper, online, in a local rental guide, etc.