It is hard to know how certain rumors get started. But the hot one in Olympia today has Gov. Chris Gregoire in line to replace Elena Kagan as solicitor general under President Obama.

Okay, Gregoire is a lawyer. And she’s a Democrat. So she’s eligible. But whether she’d be appointed is speculation. Sort of how she was mentioned as a possible Supreme Court appointee because Obama once praised former Chief Justice Earl Warren for his experience as a governor. Suddenly every female-Democratic-lawyer-governor was on someone’s list.

The sourcing on this rumor is “insiders” and was first mentioned on the Building Industry Association of Washington’s blog. Other than that, nothing. And the BIAW may be engaging in some wishful thinking since it doesn’t think much of Gregoire.

But since it’s all in fun, and it’s Monday, I’ll play.

If Gregoire resigned to go to Washington, D.C., fellow Democrat Brad Owen would move up from the lieutenant governor’s job. But when would the office appear on the ballot? If Gregoire resigns before the June 7-11 filing period, the office would be on this year’s ballot. There also are provisions for a special filing period should the vacancy occur after filing. I’m checking to see what the drop-dead date would be.

UPDATE: Katie Blinn at secretary of state’s office says a resignation prior to May 31 would trigger a primary AND a general election for the office. But a resignation after May 31 but before October 3 would set up a winner-take-all general election with everyone who files on the ballot together. Then it gets even more strange because if Gregoire resigned AFTER Oct. 3, Owen would serve until the regular 2012 election even though his vacant lieutenant governor spot would appear on the 2011 ballot.

Of course Gregoire clearly made a mistake when she endorsed Obama prior to the Washington state caucuses in 2008. Obama has, so far, only given appointments to the politicians who endorsed his rival Hillary Clinton. That would be Gary Locke and Ron Sims.

And why not combine the spring’s most-played political parlor game with this one. Would Dino Rossi stop considering a run for the U.S. Senate and start wrestling with yet-another run for governor? Would the state have to delay the filing period to give him more time to decide?

What exactly is a solicitor general? Here’s the description from the U.S. Department of Justice:

The original Statutory Authorization Act of June 22, 1870, states, “There shall be in the Department of Justice an officer learned in the law, to assist the Attorney General in the performance of his duties to be called the Solicitor General.” The Office of the Solicitor General is tasked to conduct all litigation on behalf of the United States in the Supreme Court, and to supervise the handling of litigation in the federal appellate courts. The general functions of the Office can be found at 28 CFR 0.20.