With states still gripped by a fierce recession, the lure of $4 billion in federal grant money was an incentive to be bold and make big changes to policies and laws.

But if a second Race to the Top competition only puts $500 million or so up for grabs—the amount Tennessee won in round one—the response from states will be far more muted.

That’s the problem facing Education Secretary Arne Duncan, who acknowledged as much in a speech in Minnesota. He said with so little money, he’d like the contest to focus only on districts.

Congress so far hasn’t shown interest in opening up the state-level contest to districts. So this is probably a moot point.

But, Duncan’s desire to open it up to districts calls attention to a big problem facing him and the department if they get a second round of Race to the Top funding, and it’s a mere $500 million or so, which Congress has signaled it may be willing to spend.

Race to the Top, the $4 billion stimulus version, worked so well because it was new, there was a lot of money up for grabs, and recession-battered states were desperate to get their hands on it. President Obama will probably tout all of the success during his State of the Union speech tomorrow night.

Next time around, Race to the Top won’t be new at all, and states who feel they got burned in the first rounds of competition may have little incentive to compete. There’s not a lot of money up for grabs, especially given how time consuming it is to apply for such grants. And, with states ever so slowly starting to emerge from a nasty recession, they won’t be as desperate for the funds.

So, a key question is how can the department use a relatively small amount of money to get states to propose big things?