While most Republican voters do not want President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE to face a primary challenger, he is weaker among his party than former President Obama was in 2012 in this regard, according to a poll taken in the days before Trump officially kicked off his 2020 re-election bid.

A Hill-HarrisX survey conducted June 14-15 among registered voters found that 44 percent of Republican participants believed Trump should face a Republican primary challenger ahead of the 2020 election. That number is 12 points higher than the 32 percent Democrats in a 2011 Pew Research Center survey who said that Obama should be challenged.

Support for an attempt by an intra-GOP insurgent increases to 47 percent when independent voters who lean toward Republicans are included in the sample.

Thus far, only one Republican, former Massachusetts Gov. Bill Weld William (Bill) WeldRalph Gants, chief justice of Massachusetts supreme court, dies at 65 The Hill's Campaign Report: Biden visits Kenosha | Trump's double-voting suggestion draws fire | Facebook clamps down on election ads Biden picks up endorsements from nearly 100 Republicans MORE — who was also the 2016 Libertarian Party vice presidential nominee — has come forward to challenge Trump.

The Hill-HarrisX survey found strong differences between age groups of Republican and Republican-leaning voters with younger ones much more favorably disposed toward a challenge to the president than older ones.

Sixty-one percent of respondents who were 49 or younger said that another Republican should challenge Trump in 2020 compared to just 37 percent of those who were 50 or older.

Participants also seemed to differ based on their educational attainments with less-educated Republicans being more loyal toward the president than those who had completed college. Forty-three percent of GOP and GOP-leaning independents who had less than a bachelor's degree said that Trump should face a primary challenge compared to 53 percent of those with a four-year degree or more.

Republicans under Trump have performed better among non-college educated voters compared to previous GOP candidates and worse among those with degrees.

According to 2016 exit polls, Trump performed 10 points worse among white voters who had obtained bachelor's degrees than 2012 GOP nominee Mitt Romney Willard (Mitt) Mitt RomneyTrump 'no longer angry' at Romney because of Supreme Court stance GOP lawmakers distance themselves from Trump comments on transfer of power McConnell pushes back on Trump: 'There will be an orderly transition' MORE. He did 14 percentage points better among whites who had not completed college.

Trump's standing among Republican voters remains essentially unchanged from a November 2018 Hill-HarrisX poll which found that 43 percent of GOP registered voters said that he should face a primary challenge.

The latest Hill-HarrisX survey was conducted online among a statistically representative panel of 1,000 registered voters, 404 of whom indicated that they were Republicans or independents who leaned toward the party. The sampling margin of error for this subset is 4.9 percentage points. The sampling margin of error for the Republican-only subset is 5.5 percentage points.

Respondents were asked whether they believed Trump should face a primary challenge and not whether they believed he should be nominated by the GOP in 2020.

—Matthew Sheffield

Correction: This story originally stated that Bill Weld was the 2016 Libertarian Party presidential nominee. He was the party's vice presidential nominee.