Health & Human Services Secretary Kathleen Sebelius. (Jeff Martin for The Washington Post)

The New York Times's Jeremy W. Peters reports Wednesday that, according to an anonymous source, outgoing Secretary of Health and Human Services Kathleen Sebelius (D) is looking at a potential run for Senate back in her home state of Kansas.

Sebelius was a popular two-term governor of the state, which has little in the way of a Democratic bench and hasn't recruited a big name to run against Sen. Pat Roberts (R-Kan.).

But Sebelius's path to victory is, to put it lightly, hard to see. And there seem to be all kinds of reasons for her not to run. Here are a few of them:

1) Sebelius is not (popular) in Kansas anymore

A recent poll from Democratic-leaning automated pollster Public Policy Polling shows her with a 38 percent favorable rating back in her home state, compared to 55 percent unfavorable. That's a far cry from where Sebelius was at before she left office and joined the Obama administration. Given the state's red leaning, those numbers are almost disqualifying.

2) She is the person most closely associated with Obamacare's implementation

Yes, Sebelius has ties to her state. But she's still best-known right now as the person who oversaw Obamacare's deeply flawed implementation. And in a state that went for Mitt Romney by 22 points in 2012, that's a complete non-starter.

Election Day is less than seven months away, and Republicans are making it all about Obamacare, which means that this will hardly be a distant memory.

3) Democrats have a real shot at winning the governor's seat

Gov. Sam Brownback (R) is in some legitimate trouble in his reelection campaign. Having Sebelius on the ballot risks nationalizing that race and hurting the chances of state Rep. Paul Davis (D), who Republicans would undoubtedly love to tie to Sebelius and the Obama administration.

4) She is (or at least was) friends with Roberts

Sebelius's friendly history with the state's senior Republican senator has been used against Roberts in this year's primary. Roberts recommended her for her Cabinet post and once cited their "special relationship."

Things have cooled in recent months -- owing in large part to Roberts facing a primary challenge where that "special relationship" was used against him. Roberts called for Sebelius to resign last year.

Perhaps that's motivation for her to challenge him, but it hardly means she can beat him.

Indeed, Sebelius's only real shot at victory would seem to be Roberts somehow losing his primary to physician Milton Wolf (R). But she would need to decide to run well before that would happen, and if it didn't pan out, she would be pitted against Roberts.

There have been all kinds of surprise candidates this year, with most of them coming on the GOP side: Ed Gillespie in Virginia, Scott Brown in New Hampshire and Cory Gardner in Colorado.

But it's really hard to see why Sebelius would envision any real path to victory so close to Obamacare's implementation.

Update 3:15 p.m.: Another potential stumbling block is the fact that Sebelius is still secretary and plans to be until the nominee to succeed her, Sylvia Burwell, is confirmed. It's not clear when such a vote would be, but the filing deadline in Kansas is June 2. Sebelius cannot both run for Senate and serve as secretary at the same time.