This week, the Senate is back and word is that lawmakers will start trying to figure out how to pay for the edujobs bill.

In fact, U.S. Secretary of Education Arne Duncan spent last Friday in Washington state stumping for the edujobs bill, alongside Sen. Patty Murray, D-Wash., a key member of Congress who hasn’t always seen eye-to-eye with the administration on K-12 policy issues. (For instance, last year, she spoke out against a measure that would have increased funding for the Teacher Incentive Fund—a major White House priority—because the boost would come at the expense of the formula-based grants aimed helping states improve teacher quality.)

But if Duncan wants to get edujobs through the Senate without those “wrong offsets,” he may need help from folks like Murray, who sits on both the Senate education committee and the Senate appropriations subcommittee that oversees K-12 spending, and has many fans in traditional education organizations.

And, besides helping to push edujobs, Murray and other Washington state officials may also have something to gain from face time with Duncan. Washington is hoping to snag a Round 2 Race to the Top grant even though it has no charter school law.

In fact, Murray and Duncan went to an innovative public school, in part so that the Evergreen state could show the secretary that public schools can help try out new and different approaches in the same way that charters can.

What’s more, Murray, who is up for re-election this fall, is also fending off a pretty strong challenge from Republican Dino Rossi, a businessman. She’s considered likely to keep her seat, but I’m guessing she figures a little publicity showing that she’s working with the administration to help steer federal dollars to Washington probably couldn’t hurt.