Vice President Biden speaks at a Fourth of July celebration at Independence Hall in Philadelphia. (Matt Rourke/AP)

Everyone with even a passing interest in politics has probably followed the astonishing, ­
self-inflicted downhill slide of Hillary Clinton amid the launch of her most recent memoir, “Hard Choices.”

Was Vice President Biden one of those watching? After all, he certainly has a passing interest in politics.

We’re hearing that he’s reached out to many of his hundreds of former Senate, vice-presidential and campaign staffers — and he’s run a number of campaigns, including two for president — just to say “Hi, howahya?”

A recent Democratic National Committee e-mail invite — from Biden counselor Greg Schultz, Ohio director for the Obama-Biden reelection campaign and deputy political director for that state in 2008 — was followed by a July 1 reminder from Schultz to “join the Biden alumni call” that evening and “hear from the vice president as to what he’s working on.” Schultz asked recipients to “pass the message on” if they knew people who may not have been invited.

It’s unclear how many people dialed the number to join in — the callers were on mute — but Biden popped on right on time at 7 p.m., we heard, to say that he had wanted to do this shout-out for a couple of years. He lamented that, while he saw some former aides all the time, he’s sorry he hasn’t been able to keep up with everyone.

The call, we were told, lasted just a few minutes.

Now, some people might think he’s beginning preliminary organizing for a possible 2016 run.

But, naw. We think he’s just being friendly. He even extended an invite to everyone to stop by the veep’s house for a gathering this fall.

Booker’s selfie project

Like a high-schooler collecting yearbook messages before summer break, Sen. Cory Booker (D-N.J.) is roaming the halls of the Senate before August recess asking his peers to pose for selfies.

Booker, who rose to national prominence partly through social media, may be the most selfied (can that be a verb?) politician. Next to Sen. John McCain (R-Ariz.), he has the most Twitter followers of any member of Congress — nearly 1.5 million.

Booker wants to photograph himself cheek to cheek with all 99 of his fellow senators (there’s a lot of free time on Capitol Hill these days), and he’s up to 10 since starting this project four weeks ago.

He’s posted them on his public Instagram account, but his office declined to comment on what spurred Booker to do this or what he plans to do with the photos. (A collage for his office? A my-first-year-in-Washington memory book?)

Booker makes a point of writing something nice about each colleague, regardless of party, who is willing to pose with him.

Highlights include this note about Sen. John Thune (R-S.D.): “Senator Thune has become a valued colleague and friend who challenges me on issues in constructive ways. He is also hands down in the best shape of all the Senators. 8 years my senior, his work ethic in the Senate gym shames and inspires me to get in better shape. #DudeAreYouSeriously­-

His first picture was with Sen. Angus King (I-Maine), whom Booker called “a true gentleman,” and his most recent was with Sen. Rand Paul (R-Ky.), whom Booker bonded with over “a respect for the holiday of Festivus.”

As with baseball cards, will some senators be harder gets than others? And will Booker come up with niceties to say about everyone he poses with? Even Sen. Ted Cruz (R-Tex.)?

Monica? We didn’t say it.

On Friday, a Reuters reporter tweeted a picture of a bumper sticker reading “Monica’s Lewinsky’s X-Boyfriend’s Wife for President.” At the bottom it said: “Authorized by the Republican Party of Virginia.”

But no, it wasn’t.

Garren Shipley, spokesman for the state GOP, said there is a political strategy in place this year, “and it does not involve that.” The sticker, he said, appears to be “an amateur effort.”

“We’re focused on 2014, and if she’s the nominee in 2016 we’ll have a lot to say then,” he told the Loop on Friday.

Though Hillary Clinton has said she’s “moved on” from the Lewinsky scandal of the late 1990s, it’s impossible to imagine a campaign without such quips, should she choose to run.

But, just to be clear, the one that is apparently making the rounds in Virginia is not official Republican Party material.

Also, that line is not new. Several vendors are selling T-shirts online with the same quote.

Good to know we can expect only the highest levels of political discourse ahead of 2016.

$0 for the other guy

Everyone loves to back a winner. And Charlie Dent is a pretty sure bet.

Rep. Dent (R-Pa.) boasted one of the best fundraising quarters of his congressional career. He hauled in more than $400,000 this spring.

“It is humbling to receive such strong support for my reelection,” the five-term congressman said in a statement.

The release is pretty standard end-of-the-financial-quarter fare — such notices have reliably begun to trickle in this week — except for one thing: Dent doesn’t really have a reelection campaign. He’s running unopposed.

Reports aren’t due to the Federal Election Commission until Tuesday, so we couldn’t see Dent’s itemized contributions. His campaign tells us a little more than half — $214,812 — came from individuals, while $188,812 was from PACs and other organizations. Top contributors are said to be big-business types such as Norfolk Southern and Merck.

David Wasserman, who handicaps House races for the Cook Political Report, said the generous support is symbolic because Dent, a moderate, is “the de facto leader of the Main Street mind-set.”

A significant chunk of incumbents are not facing a challenge heading into November. In the 31 states that have held their primaries, 48 incumbents out of 273 will be unopposed, according to the University of Virginia Center for Politics.

Without the risk of losing their job, does that give them more or less incentive to get work done?

— With Colby Itkowitz

Twitter: @KamenInTheLoop, @ColbyItkowitz