DC is in a precarious position. They have no Senators or opportunity to vote for ones. They get to vote for a federal representative in the House, but that member has no voting rights (except on procedural votes). They have a mayor and city council, but the federal government has the final say on everything that is done within the city. They can't raise taxes on their own or build more transit lines without approval from Congress. It is a strange quandary for the capital city of a country to have taxation without representation, when that country broke off from its colonial master for that very reason.
Republicans do not want DC to have statehood for the same reason that they do not want Puerto Rico to have statehood: Because they would almost assuredly elect 2 Democratic Senators.
Unlike Puerto Rico though, DC does have something to trade: Electoral Votes. Washington DC has 3 electoral votes like it would if it had a state because of the 23rd Amendment to the Constitution. Puerto Rico has none, because it is simply a territory.
DC could become part of Maryland for all intents and purposes. They would give up their 3 electoral votes in exchange for having administrative and voting functions transferred from Congress to the State of Maryland. Maryland would gain no additional Senate seats for DC, but their Senators would be responsive to the needs of DC. Maryland would probably gain a single member of the House of Representatives that would represent the city and some its suburbs in Maryland. The mayor and city council of DC would work with the State of Maryland instead of Congress, as cities normally do.
The people of DC win. The people of Maryland win. The Republican Party nets a couple of electoral votes. It works out well for almost every one.