Acting President Glen Allen Walken had no problem with it.
Could somebody who would be next in the line of succession for POTUS actually refuse to serve?
Sure, under the 25th Amendment all he would have to do is say he’s “unable to discharge the powers and duties of his office,” and the presidency goes to whoever’s next in line.
Side note: I’m currently reading *1948, *about Truman’s election, by David Pietrusza. He says that after the Democrats’ humiliating defeat in the 1946 mid-term elections, there were serious calls for Truman to appoint the Republican Robert A. Taft to be Secretary of State (under the law at the time, SoS was next in line for the presidency) and then resign, making Taft President, to satisfy “the people’s mandate.”