The e-mails came steadily over the weekend, hitting the in-box with tantalizing memo lines: "Mitt's VP" and even "My VP."

Alas, these were not introductions to Mitt Romney's running mate but fundraising appeals and promotions for a contest to meet the VP choice. The contest was first announced last week in a pitch from Matt Rhoades, Romney's campaign manager.

"I've got an important choice to make. Sometime soon, I will be choosing a vice presidential candidate to join our winning ticket," Romney wrote in one of the e-mails, promising the GOP ticket will be "America's Comeback Team."

Who will be Romney's running mate is a closely guarded secret, perhaps known only to the presumptive GOP nominee and Beth Myers, his trusted long-time aide who is handling the search. And when the Romney decision will come is also anyone's best guess.

The New York Times reported today, in a story about what Tim Pawlenty has to offer if he's the VP pick:

Mr. Romney has reached a decision, his friends believe, and he may disclose it as soon as this week.

Well, alrighty then.

Why the speculation about this week? Romney is headed to London for the July 27 opening ceremonies of the Olympics and then to Israel for meetings with Prime Minister Benjamin Netanyahu. So these are the last few days he's in the United States before heading overseas for a week or so.

Stories about potential running mates are popping up with frequency. Some conservatives, especially those who oppose abortion, were in a tizzy about a Drudge Report item last week saying former secretary of State Condoleezza Rice is a top contender.

Today, Sen. John Thune of South Dakota acknowledged to The Hill that he's traveled to Boston to meet with Myers -- but not about the VP pick. The Hill story says Thune, who endorsed Romney early on and campaigned for him in Iowa in the run-up to the caucuses, has "re-emerged as a viable vice presidential candidate."

Ohio Sen. Rob Portman is in for a round of stories about his VP chances, as he headlines a news conference in Cincinnati today aimed at bringing attention to President Obama's trip there.

And what about Pawlenty, the former Minnesota governor who was on John McCain's running mate short list in 2008? Pawlenty not only gets the NYT treatment today, he was one of three Republicans featured in thousands of pages of opposition research by a Democratic super PAC that was released on Friday. Portman and Florida Sen. Marco Rubio were the others.

Stay tuned.