Most news accounts of budget negotiations between the White House and Congress focus on two men: President Obama and House Speaker John Boehner. The man who ran on a platform of “balanced” deficit reduction, and the man who represents the party that refuses to increase taxes on high earners.

But there’s a third agent, quietly keeping the negotiating center of gravity in Democrats’ comfort zone.

On Tuesday, House Minority Leader Nancy Pelosi will file what’s known as a discharge petition — a procedural tool that will increase pressure on Republicans to allow Bush tax cuts for top earners to expire. If 218 members sign the petition, legislation to permanently extend middle-income tax cuts will get a vote, and Republicans will be on the spot. Leadership aides expect nearly every Democrat will put pen to paper in support of it, and then push squishy Republicans to break with leadership and sign it as well.

That reflects half of Pelosi’s role. The other half is subtler. As the controller of an overwhelming number of Democratic votes, she’s there to warn all negotiators, including Obama himself, not to cut a bad deal.