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Veepstakes Intrigue Deepens as Clock Ticks on Candidates’ Picks

The always-unpredictable Donald Trump added a bit more intrigue to his vice-presidential search on Monday in the way that only Trump can: With a trio of tweets.

In one, Trump praised Sen. Tom Cotton for his interview on NBC's "Meet the Press," in which the Arkansas senator attacked Democrat Hillary Clinton but seemed notably lukewarm on Trump. In another, Trump said he was "very impressed" with Indiana Gov. Mike Pence, with whom he met this weekend.

And Trump used a third to announce a surprise meeting with Iowa Sen. Joni Ernst, a candidate not thought to be high up on his list of vice-presidential prospects.

Those tweets capped a weekend full of vice-presidential vetting activity on both sides of the aisle, as Trump and Clinton head into the final weeks before their respective party conventions.

Related: VP Watch: July 4, 2016

Three potential Democratic vice-presidential candidates — New Jersey Sen. Cory Booker, Secretary of Labor Tom Perez and Ohio Sen. Sherrod Brown — appeared on the Sunday talk shows this weekend, a traditional rite of vetting that allows candidates to show off their surrogate skills. Booker, for the first time, did not deny he was being vetted by the Clinton campaign, which observers read as an implicit confirmation he's in the mix, while Perez's occasionally meandering, repetitive interview on NBC's "Meet the Press" raised doubts about his viability.

Trump Vetting Vice-Presidential Picks Just Weeks Ahead of Convention 1:50

But with just just over two weeks until Republicans kick off their national convention, the VP decision is most urgent for Trump, and two sources tell NBC News that he's is expected to announce his pick later next week. That's later than many initially expected, and runs right up against the start of the convention. But the thinking among Trump's advisers is to allow last week's rough news cycle for Clinton — which saw her sit for a three-and-a-half-hour meeting with the FBI over her use of a private email server as secretary of state — continue into next.

Still, there's certain to be lots of activity — and lots of attention — focused on Trump's pick, as he has yet to meet with former House Speaker Newt Gingrich and New Jersey Gov. Chris Christie, both believed to be at the top of his list, as well as a handful of other second-tier possibilities.

Trump will check another box on his list Tuesday when he campaigns in North Carolina, where NBC News has learned Tennessee Sen. Bob Corker will join Trump at his rally in Raleigh.

The first confirmed vice-presidential prospect to meet with Trump, Indiana Gov. Mike Pence, recounted his meeting to reporters in Indiana this weekend.

"He was very interested in the progress of the state of Indiana as much as I was interested in his plans for the future," Pence said.

Pence, his wife and their daughter met with the presumptive GOP nominee and Melania Trump at Trump's golf course Saturday in New Jersey, where Pence said Trump "beat me like a drum" on the golf course. The Trumps "couldn't have been more kind and gracious," he added.

Beyond that, Pence offered few details, but notably wouldn't confirm whether he'd take the job if offered, saying only "I'm not gonna get into hypotheticals." Pence also repeatedly declined to comment on the controversial tweet Trump issued this weekend attacking Clinton, which featured a picture of a Star of David over a backdrop of $100 bills and appears to have gained traction on a white supremacist listserv.

Related: Who Will Donald Trump Pick as His VP?

The other potential VP picks who spoke out this weekend all downplayed their chances or seemed less than enthused about the presumptive GOP nominee. Cotton in fact declined to say why Trump is a better candidate than Clinton, saying that Trump "make the case for himself," despite Trump's tweet. Ernst's meeting with Trump was a "last-minute" surprise, according to a source close to the senator, and she said only in a statement that she had a "good" meeting with Trump where they discussed what she hears from Iowans on her travels. She said she plans to continue to "share my insights" with the candidate on the economy and national security.

And Gingrich, speaking at the Aspen Ideas Festival on Saturday, called all the chatter around his chances "wild speculation." Still, he proved a strong surrogate for Trump, touting the candidate's disruptive presence in the political sphere and telling NBC News that the fact Trump's being considerably outspent on the airwaves by Democrats won't be an issue for him.

Trump's pick will be closely watched, as many Republicans are hoping his vice president will not only help balance out the ticket politically but balance out Trump personally.

In addition to strengthening Trump's support in key swing states or among untapped demographic groups, skeptics are hoping he'll pick a candidate who can be a steady hand on the stump, one with strong conservative credentials and a long history with the GOP.

Ron Bonjean, a longtime GOP strategist, said Trump's efforts to build out a general election campaign in recent weeks have been encouraging but not enough to fully ease the concerns many Republicans still have with him.

"If he were to pick a vice president that is competent, has experience both in office and with the party and could relate to Americans, that would go a long way," he said.