With the 2012 GOP primary candidates set for the big Tea Party Express debate tonight, top Democrats, including some at the White House, are keeping an eye out for a key dynamic that could play a major role in determining the outcome of the war over Obama’s new jobs bill.

Specifically: The House GOP leadership is sending new and conciliatory messages about working with President Obama to get parts of his jobs plan passed. Will those messages get stepped on by the 2012 GOP primary candidates’ ever-escalating anti-Obama rhetoric, drowning out House GOP efforts to strike a more compromising tone?

Dems are eying the possibility of a schism between Congressional GOP leaders and the party’s political leadership, including the 2012 candidates and the heads of the party committees, who are expected to strike an increasingly strident and uncompromising tone towards Obama’s new jobs plan.

With Obama vowing to take his jobs bill to the American people, House GOP leaders have gone out of their way to signal a willingness to work with the president. Boehner today pledged a “careful examination” of Obama’s plan, adding: “It is my hope that we will be able to work together to put in place the best ideas of both parties and help put Americans back to work.”

Whatever the true intentions of the GOP leadership towards Obama’s plan, the tonal shift signals a recognition that Republicans must appear prepared to work with Obama on jobs, and must not be seen rejecting his ideas wholesale.

Contrast that with the tone taken by Republican National Committee chair Rience Priebus, who dismissively declared: “Once again, another speech from Obama making the exact same promises he did before the first stimulus.”

In all likelihood, the 2012 GOP candidates will increasingly adopt such language and worse, bashing the jobs bill wholesale in an effort to appeal to GOP primary voters — particularly with a Tea Party debate set for tonight. What’s more, this potential schism goes beyond just a divide between the Congressional leadership and GOP candidates and political operatives. As Jonathan Cohn notes, conservatives in Congress have also struck a far more aggressive tone towards the jobs bill than the GOP leadership has.

How does this all impact the prospect for the jobs proposal itself? Unclear. On the one hand, a divided GOP might struggle to send a unified message on jobs, giving Obama more leverage as he pushes Republicans to pass his plan. On the other, having the 2012 GOP hopefuls out there uniformly trashing the jobs bill could make it less likely that the House GOP rank and file will embrace even parts of it if the leadership appeals for their support. Either way, the prospect for GOP division over the American Jobs Act is a key dynamic Dems will be watching.