Mike Pence a 2020 favorite after vice presidential debate

The vice presidential debate Tuesday, full of sharp barbs and head shakes, was largely ruled a win for Donald Trump's running mate, Mike Pence, but many pundits agreed that he helped himself – and his future political prospects – more than he boosted the current Republican ticket.

A new poll out Friday shows the analysts were right: Pence, the governor of Indiana, topped the list for whom Republicans would like to see as their nominee in 2020 if Trump loses in November.

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The Politico/Morning Consult poll found 22 percent of Republican voters would want to see Pence at the top of the ticket in four years, compared with 13 percent who said they would want to see Trump give it another go.

House Speaker Paul Ryan, R-Wis., who was Mitt Romney's running mate on the GOP ticket in 2012, would also be the choice of 13 percent.

Heated moments from the vice presidential debate

Texas Sen. Ted Cruz, who came in second place to Trump in the Republican primary this year but angered many party faithful by pointedly refusing to endorse Trump at the Republican National Convention, is favored by 12 percent of Republicans. Florida Sen. Marco Rubio, who also ran unsuccessfully for the 2016 nomination, earned 11 percent support.

Survey respondents said Tuesday night's debate had a significant impact on how they see Pence, with a majority of all registered voters – 52 percent – saying they now have a more favorable view of the candidate. Thirty-three percent said they have a "much more favorable" impression of him.

Republicans are particularly pleased with Pence, with 79 percent saying the debate improved their view of their vice presidential nominee. Nearly 1 in 3 Trump supporters said they would prefer to vote for Pence at the top of the ticket, rather than Trump.

Overall, however, the debate seems to have had almost no impact on the shape of the race. A whopping 84 percent of registered voters said the debate did not change who they plan to vote for on Nov. 8.