If the Democrats enact a big stimulus package that seems to save America from a second Great Depression, what would that do to the Republican Party?

Dean Baker suggests the GOP fears being out of power for a generation if the Democrats are seen to have that success. So how can the GOP deprive the Dems of that aura? By getting involved, voting for the bill, and sharing credit for success? By blocking the bill and hoping we won't have a deep, unforgettable recession or worse? Generally speaking, what other choices does it have?