(CBS News) — Whether or not they’re voting for him, 65% of registered voters nationwide think President Trump will definitely or probably be reelected, including more than a third of Democrats who think so. Republicans are especially optimistic: more than 9 in 10 expect him to win.

Still, potential head to head matchups with all the major Democratic candidates against Mr. Trump show a tight race no matter who the Democratic nominee is, with no more than three percentage points separating the Democratic candidates from Mr. Trump in any matchup with the six top polling Democratic contenders.

Most voters have dug in. When it comes to who they will vote for in November, 6 in 10 voters say it doesn’t matter who the Democratic nominee is, or what Mr. Trump might do over the next year.

Despite these close matchups, no Democratic candidate gets more than about a quarter of voters who thinks they would probably beat Mr. Trump (Bernie Sanders does best at 27%). Republicans are particularly confident of Mr. Trump’s chances: large majorities think each of these potential Democratic opponents would be long shots to beat him in November. Democrats are less sure of their party’s chances. They express the most confidence in Joe Biden and Sanders, but fewer than half of Democrats think any of the candidates is above a “maybe” to win.

Measuring sentiment among would-be Democratic primary voters nationwide, it’s Sanders who is leading in overall preference to be their nominee.

But just 42% of Democratic primary voters have definitely made up their minds at this point — and of course many won’t get a chance to vote until later this spring. Just over half are enthusiastic about their first choice picks. Elizabeth Warren‘s (69%) and Sanders’ supporters (65%) are the most enthusiastic, while just over half of Biden’s supporters (53%) and Pete Buttigieg‘s supporters (52%) are enthusiastic as well. But just over a third of Bloomberg’s and Amy Klobuchar‘s supporters are enthusiastic about their candidates.

Democratic voters see Sanders (57%) and Warren (53%) as the candidates who will fight the most for people like them. Though Sanders leads overall, Democratic primary voters — as well as likely general election voters — pick Warren as the candidate who has impressed them the most in recent debates. Fifty percent of Democratic primary voters rated Warren’s performance as impressive, ahead of all the other candidates, with Sanders named by 42%. Bloomberg was at the bottom, with just 15% saying his performance impressed them.

Most Democratic primary voters (62%) expect to have an influence on deciding who will be the eventual nominee when their state holds its primary or caucus, but they are more divided when it comes to how their party should approach the 2020 election. Fifty-four percent want the party to advance a more progressive agenda than the country had under President Obama, while 46% favor a return to the way it was before Mr. Trump took office. Sanders leads among the first group, while Biden leads among the second.

This CBS News survey is conducted by YouGov between February 20-22, 2020. A nationally representative sample of 10,000 registered voters was selected, including 6,498 self-identified Democrats, as well as independents who plan to vote in the Democratic primary this year. This sample was weighted according to gender, age, race, and education based upon voter registration lists and the U.S. Census Current Population Survey, as well as the 2016 presidential vote. The margin of error for the entire sample is 1.2 points. For the sample of likely Democratic primary voters it is 1.7 points.