(CN) – More than 4-in-10 Republicans want a GOP candidate to challenge President Donald Trump in the 2020 primary, according to a new survey that calls into question the likelihood of success of his re-election campaign.

A Monmouth University poll released Monday found that 43 percent of Republican voters said they would like to see Trump face off against another Republican, while 49 percent said they would like to see him run unopposed.

Despite supporting a contested primary, those same Republicans said they would vote for Trump if he was challenged by either Texas Sen. Ted Cruz or former Ohio Gov. John Kasich. In a hypothetical race between Trump and Cruz, the respondents said they would vote for Trump 43 percent to 37 percent. Between Trump and Kasich, that number would increase to 47 percent versus 33 percent for Kasich.

Among all Republicans, Trump had 66 percent support versus 21 percent for Cruz and 73 percent to just 14 percent for Kasich.

“It’s not clear that any Republican, whether a past challenger or new blood, would have a realistic shot at taking the nomination. The party’s base belongs to Trump,” said Patrick Murray, director of the Monmouth University Polling Institute in a statement.

President Trump may face an uphill battle to be re-elected in 2020. Just 38 percent of all registered voters polled said Trump should be re-elected, compared to 57 percent who said someone else should be in office. Those results are similar to the same question asked of registered voters in November 2018.

On the Democratic side, Democrats said they are looking for a candidate who will be a strong contender against President Trump. Over half of Democrats and independents who lean Democrat said they prefer someone who stood a good chance to beat the president, even if they disagree with the candidate on the issues.

“In prior elections, voters from both parties consistently prioritized shared values over electability when selecting a nominee. It looks like Democrats may be willing to flip that equation in 2020 because of their desire to defeat Trump. This is something to pay close attention to when primary voters really start tuning into the campaign,” Murray said.

While a number of Democrats have announced their campaign for the presidency or exploratory committees, the poll found that former Vice President Joe Biden has the most support by those polled, at 29 percent of Democratic voters. Biden has not made any announcements about running for office.

Biden was followed by Vermont Sen. Bernie Sanders at 16 percent and 11 percent for California Sen. Kamala Harris. “As with any presidential nominating contest at this point in time, voter preferences are driven largely by name recognition. It would be very unusual if these results don’t change substantially when we get closer to next year’s primary contests. These early polls are most useful for looking at each candidate’s profile among the party faithful to assess potential viability,” Murray said.