Elizabeth Warren: A good running mate for Hillary Clinton?

Sen. Elizabeth Warren (D) of Massachusetts and presumptive Democratic nominee Hillary Clinton held their first joint campaign appearance Monday morning.

For supporters of Senator Warren as a pick for vice president, the campaign stop in Cincinnati is an opportunity to show how she would be as Mrs. Clinton's running mate, if she does, in fact, want the job.

Warren speaks directly to the progressives who gave Vermont Sen. Bernie Sanders' campaign its unexpected strength. But could she connect with the rest of the electorate and support the implementation of Clinton's agenda, if the team were to win the White House in November?

As the Senate's leading voice for tougher oversight of Wall Street and a hero of the Sanders camp, some political analysts say that Warren could help Clinton break with her reputation as being too closely tied with Wall Street. Warren has proven her ability to articulate a progressive counterargument to presumptive Republican presidential nominee Donald Trump, beyond blasting him as a "racist bully" and "a small, insecure, money grubber."

"One reason that Warren has been such an effective surrogate this month is the reminders she gives her audiences of the essential dehumanization of the financial crisis, of the vulture-like role that Trump and his class played in the lives of ordinary people," Benjamin Wallace-Wells wrote for The New Yorker, saying Warren effectively channels the economic populism that has emerged at the forefront of this election season.

"Warren, with everything she's done these past few weeks, has made it really hard for her not to be looked at," Mary Ann Marsh, a Boston-based Democratic strategist, told the Associated Press. "She has demographic pull. She's got the economic portfolio and no one's taken on Trump better."

One downside of Warren's tough rhetoric, however, is the fact that she alienates many of the centrists Clinton hopes to attract, particularly the "Rockefeller Republicans," fiscal conservatives who may yet be seeking an alternative to Mr. Trump.

As was made apparent during the Democratic primary, Senator Sanders' economic messages were a rallying cry for young, white liberal voters, rather than minority voters, so Warren wouldn't necessarily draw in new demographics for Clinton, especially when compared to other candidates on the vice presidential shortlist.

Former Virginia Gov. Tim Kaine is a moderate and widely liked, and could help pull in Virginia voters – a key swing state – as well as independents. Julian Castro - former San Antonio mayor and current secretary of Housing and Urban Development – would be the first Hispanic on a major party ticket, posing a striking contrast to Trump's statements on Hispanics and potentially inspiring new Latino voters to turn out at the polls.

Another strike against Warren is that bringing her to the White House would cost the Democrats a seat in the Senate, at least at the beginning of Clinton's presidency, because her seat would be temporarily filled by an appointee named by Massachusetts' Republican governor Charlie Baker until a special election can be held.

But perhaps the greatest weakness of having Warren on the ticket, say political analysts, is that the senator so far hasn't indicated a willingness to fall in step with Clinton's world views. "The Massachusetts senator also has her own national following, her own loyal advisers and her own well-thought-out worldview," as Amy Chozick and Jonathan Martin wrote for The New York Times. She didn't endorse Clinton until this month, referring to her repeatedly as a "fighter" but stopping short of praising her as a champion of working families.

"In the current era of presidential politics, social media has allowed more people to assume the role of attack dog that was traditionally left to the vice-presidential nominee," said Jason Rosenstock, an analyst at Thorn Run Partners who covers the financial industry, told Politico. "Warren has shown an excellence in the platform that would allow her to help the campaign incredibly while maintaining her growing position of power in the Senate."

In other words, Warren – and Clinton – may see more benefits in continuing in her current role, than as a candidate for vice president.