With Mitt Romney overseas on a gaffe-ridden jaunt, his would-be deputies are taking up the campaigning slack back at home, jockeying for position as they press the flesh on the campaign trail.

Tim Pawlenty, Rob Portman, Bobby Jindal and Marco Rubio – all mentioned to a greater or lesser degree as potential vice-presidential picks – are all in swing states over the weekend, participating in events designed to bolster support for the Republican ticket.

But with the presidential candidate himself winging it to Israel for a reception he hopes will be better than the one he received in London, the coast is clear for one of the would be running-mates to start, well, making the running.

Of the crop being touted, Ohio senator Rob Portman is the man that the clever money appears to be settling on.

His stock rose on Friday with the intervention of leading Republican congressman John Boehner.

In an interview with Fox News, the House speaker vouched for his long-standing friend and fellow state politico.

"I'm partial to Rob Portman," Boehner told Fox's Greta Van Susteren, adding: "I think he'd be a great asset for Governor Romney.

While Portman campaigns in Ohio, his potential rivals for the vacant post of Romney's running-mate are doing likewise across the country.

Louisiana governor Jindal is set to headline an event in Coral Springs, Florida, with Pawlenty, a former Minnesota governor, heads to North Carolina.

Meanwhile Rubio will be holding a Romney "victory rally" in Las Vegas. The Florida senator is one of the most high-profile Hispanic members of the Republican Party and is thought, by a few, to represent a savvy outside punt for the vacant VP spot.

On Friday, former New York mayor Rudy Giuliani said he thought Rubio to be "the most exciting" candidate being talked about.

He added in an interview with Tampa's News Channel 8: "[Rubio] is of a different generation. He makes outreach much more possible to a younger people – people in their 30s where the Republican Party has a little bit of a deficit."

But the man himself has previously ruled himself out. Likewise, Pawlenty – who fits the mould of a safe, if a little dull, right-hand man – has said the job is not for him.

But "no" doesn't necessarily mean "no" when it comes to answering the VP call.

In addition to the quartet of Jindal, Pawlenty, Portman and Rubio, Republican senator John Thune, Rep Paul Ryan and Governor Nikki Haley are all out and about over the weekend.

It makes for a crowded field of potential picks vying for attention while Romney is away.

The Republican candidate has yet to announce a shortlist.

But in a tweet on Friday, Romney aide Beth Myers perhaps provided a clues. Amongst a list of Tweeters she suggested people follow were Pawlenty, Jindal, Rubio, Ryan, Portman and Thune.

She also threw in the names of New Jersey governor Chris Christie, former House speaker Newt Gingrich, and ex-secretary of state Condoleezza Rice in the "follow Friday" message.

As the weekend progresses, eyes will be on who appears to be performing best during Romney's absence.

"Absolutely this is an audition," explained Republican pollster Dan Judy. "They have been auditioning for the last few month. But I think how they do on the campaign trail with Romney out of the country will definitely matter when it comes down to making a choice."

He added: "Portman is widely viewed as a smart, competent person. He may not be the most exciting person in the world but he would be a good choice."

"I think you would get even odds on Portman, and Pawlenty will probably be in the final two. Rubio and Jindal are longer shots," Judy said.