Assuming your landlord is not under rent control (rents 4 or less apts.), then rent can be raised to any reasonable amount after 30 days written notice to tenant (counting days from rent due date). Raising it 28% after 2 years may not be reasonable and, in fact, may be in retaliation for not signing a lease. This can be contested 2 ways: one is to file a Tenant/Petition complaint with DCRA (Dept of Consumer & Regulatory Affairs); the other is to pay the old rent, let landlord sue you for non-payment, and then bring this matter up as a defense in that suit.
If your landlord has a registered exemption from rent control and you are month to month nothing legally prevented from increasing your rent. You can always try to negotiate with him and discuss how you can make things work better. But look around at market rents for your neighborhood for similar properties. Is the increase reasonable? Rents are increasing in DC and in some areas more than others. Figure out what it would cost you to rent another similar property so your negotiations are informed.
If there is no agreement as to rent, they can ASK for whatever they want, but if you don't agree to pay it, they'd have to prove in court that what they are requesting is the fair rental value for the apartment.
Might be worth trying to figure out what similar apartments in your neighborhood are going for.
LEGAL DISCLAIMER Mr. Borbely is licensed to practice law in the District of Columbia. His response in this forum is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question.