This could happen during times especially hard for the nation, such as after the WWII, and when no other alternatives were really available.
For example, when Eisenhower was asked to be the president, the current president, Truman, was very unpopular. Truman was a Democrat, and the democrats did now believe he could win re-election, and as Eisenhower was very popular at the time they tried to win him over to their side. In the end however, Eisenhower run as a democrat.