CNN —  

Sen. Elizabeth Warren moved up to a second-place tie with Sen. Bernie Sanders nationally, but both remain behind former Vice President Joe Biden, who also tops the list of who people think would beat President Donald Trump, according to a new poll from Monmouth University.

In another poll, Biden leads the Democratic field at 30%, followed by Sanders at 15%, and Warren at 10%, according to a Suffolk/USA Today poll released Wednesday.

The Monmouth poll found Biden is currently leading others in the primary, with 32% support from Democrats and Democratic-leaning independents, followed by 15% for Warren and 14% for Sanders. Warren has moved up five percentage points from Monmouth’s May poll, and Sanders moved down one point.

Biden is winning the perceived electability game, according to Monmouth. Biden scores a 7.7 among Democratic voters when asked the likelihood the potential nominee could beat Trump next year (with 0 meaning he would definitely lose to Trump and 10 he would definitely defeat Trump). Sanders and Warren follow with scores of 6.5 and 6.4.

When asked about Democrats in 2020, most people are “excited” to see Biden run (51% of Democrat and Democratic-leaning independent voters), followed by 41% for Sanders. Despite Sen. Kamala Harris’ consistent placement as fourth or fifth in polling, she took third on excitement. Two in five were “excited” to see her run, just a few points higher than Warren (37%).

Two in five Democratic voters want New York Mayor Bill de Blasio to drop out of the race.

But Democratic voters say their support is contingent on the debates – 86% said the candidate debates will be very or somewhat important in determining who they’ll support for president. Eight in 10 Democrats in the Suffolk poll and six in 10 in the Monmouth poll planned to watch the Democratic debates. Monmouth’s respondents were lower since they included an option to “watch live clips later” (a quarter of Democrats said they would do that).

There’s high approval for the Democratic National Committee’s decision to limit the first debates to 20 candidates – three quarters of Democratic voters said they were in favor. But there’s a divide in the party if one or two more candidates meet the qualifications. If 21 or 22 candidates meet qualifications, 49% of Democratic voters said the DNC needs to enforce the rules and limit the number to 10 a night, but 45% said they should just let an extra person on stage.

Voters say they want their candidates to focus on issues other than the President. According to the Suffolk poll, 20% of Democratic voters cited health care as the single issue they want to hear discussed by the candidates in the first debate, followed by 12% who said immigration and border security and 9% for the economy and budget.

Among Republican and Republican-leaning independent voters, 90% plan to support Trump in a Republican primary, while just 5% support former Massachusetts Gov. Bill Weld, according to the Suffolk poll. Three in five do want to see a debate among the Republican candidates for president.

Almost half in the Suffolk poll approve of the job Trump is doing as president. Trump’s uptick in approval isn’t unprecedented – other polls have shown similar movement. The Suffolk poll is slightly more positive than other polls, but seems to be capturing a slight improvement in approval.