There may be special legal privileges granted to people leasing an apartment in your jurisdiction, but generally speaking, what the owner has to provide is a habitable dwelling that conforms with the terms of the lease. Not having a phone line does not make a dwelling uninhabitable (unless your locale specifically says so). In California, it is required that the landlord maintain at least one jack and working lines (this is a direct requirement, not expressed in terms of habitability). Not in Chicago (warning: obnoxious talk occurs on that page). Lease terms generally indicate that the owner is responsible for maintaining the "infrastructure" such as wiring.
Given the added information about locale, we can turn to relevant Colorado law. §38-12-505 does not suggest that broken phone lines render a residence uninhabitable. §38-12-212.3 states that
(1) (a) Except as otherwise provided in this section, a landlord shall
be responsible for and pay the cost of the maintenance and repair of:
(I) Any sewer lines, utility service lines, or related connections
owned and provided by the landlord to the utility pedestal or pad
space for a mobile home sited in the park
but it's not clear on the face of it if that helps. There are two reasons why it doesn't. First, the typical understanding of "utility line" pertains to wires or pipes outside the building, which does not help you. The other problem is that this section is under the Mobile Home Park Act, meaning that the clause is intended to apply only to mobile home parks.