Without clarifying who the President is (McCain and Romney will have very different ideas on the economy, for example), what the GOP primaries were like, and what other parts of the Kerry Presidency went like, it's hard to speculate without making broad generalities that will get this thread moved to chat. Also, it's impossible to ignore that Kerry would have a much harder time getting TARP through Congress than Bush did, since it involved so much Federal intervention, and even in OTL, it was like pulling teeth to get Republicans to support the bill-- a precondition by OTL Democrats to support the legislation so they wouldn't get blamed. ITTL, since Kerry is running for reelection, the Republican congress many be content to let things slide off the cliff to get a wave election, so [X Republican President] may be inheriting a full blown depression and not just a recession.
Also, Obama spent a fair amount of capital on the Recovery and Reinvestment Act, so I don't know if it's fair to limit a Republican President to one signature item. You could see something like a very large corporate and capital gains rate tax cut (in contast with Obama's payroll tax cut to fight the recession) justified along Keynesian principles, as well as item that is attached to that President specifically, such as a hypothetical President Ryan attempting to change Medicaid to a block grant or encourage state experimentation on some other parts of the Federal safety net.