Buried on page 1321 of President Obama's new budget is a sign the White House is ready to play hardball with Speaker John Boehner (R-Ohio).

Fox News has learned the president is trying to zero out funding for the D.C. Opportunity Scholarship program, a $60 million program which helps underprivileged children in Washington get vouchers for private schools and has been vehemently opposed by teachers' unions.

The program has been a pet project of Boehner, who even invited some of the kids who benefit to sit in his box at the State of the Union to highlight its effectiveness and undoubtedly make a political point. The program has also won support across the ideological spectrum from Sen. Dianne Feinstein (D-Calif.) and Sen. Joe Lieberman (I-Conn.).

Lieberman told Fox News he's "very disappointed" the president wants to zero out the program but is vowing to fight to keep it alive after more than 700 D.C. families showed up for an event last month to get applications for the next school year.

"I am committed to ensuring that this valuable program gets the support it needs and deserves," said Lieberman.

A Boehner aide said the Speaker is not happy that the White House is reneging on a deal cut last April to re-authorize the program for five years, and the move is "definitely something we noticed" as an effort to take aim at the leader.

A senior administration official downplayed any tension with Boehner. "What we do this year is consistent with our budget proposals of the last three years -- we support funding so the kids now in the program can stay in the program but, otherwise, winding it down."

Earlier on Monday at his daily briefing with reporters, White House Press Secretary Jay Carney had insisted the president still wants to work closely with Boehner on a much broader "grand bargain" budget deal.

"I suppose there are many ways to make the process better, but the principal one is for elected officials of goodwill to decide that they're going to check the ideological baggage at the door when they go into negotiate," said Carney, adding: "It was the approach the president took in the discussions he had with Speaker of the House John Boehner. And it’s the approach that we would take tomorrow if there were willingness to acknowledge that there is a way to do this that's fair and balanced."