(CNN) California Sen. Kamala Harris is surging both nationally and in Iowa, according to two new polls released Tuesday.

Former Vice President Joe Biden still leads the Democratic field in the early caucus state in a poll taken after last week's debates from Suffolk University and USA Today , with 24% support. But Biden is followed by Harris (16%) and Massachusetts Sen. Elizabeth Warren (13%).

In a CNN/Des Moines Register/Mediacom Iowa poll conducted in early June, Biden was also at 24% support among likely caucusgoers, Vermont Sen. Bernie Sanders at 16%, Warren at 15%, South Bend, Indiana, Mayor Pete Buttigieg at 14%, and Harris at 7%. CNN on Tuesday released a national poll conducted with SSRS finding Harris increasing in her share of the vote, while Biden loses support.

But Suffolk's new poll suggests a decrease in support for Sanders and Buttigieg, at 9% and 6%, respectively. These differences could be because the polls weren't conducted by the same pollster and sponsor, but it's more likely that Harris is experiencing a bump in support after her performance in last week's debates, while Buttigieg and Sanders saw slight decreases.

And Quinnipiac's new national poll reflects that bump for Harris, with an increase from 7% in its early June poll to 20% support after the debates. Unlike in Iowa, Biden lost support nationally, down from 30% to 22%. Sanders also decreased slightly (from 19% to 13%), while Warren held steady.

Among those likely Democratic caucusgoers in Iowa who watched both nights of the debate, half said Harris did "better than expected," followed by former Housing and Urban Development Secretary Julián Castro (29%) and Buttigieg (22%).

On the other side, those who watched both nights said Biden did "worse than expected" (41%), as did Sanders (23%), and former Texas Rep. Beto O'Rourke (16%).

Among Democrats and Democratic-leaning independents nationally, 47% said Harris did the best job in the debates while 16% said author Marianne Williamson did the worst, followed by 15% for Biden, according to Quinnipiac.

These results don't necessarily reflect solid preferences among Democratic caucusgoers in Iowa, with 60% of likely Democratic attendees saying they might change their mind on who to vote for before the caucuses.

Those who didn't choose Biden as their first or second choice said it was because they didn't have enough information/hadn't made up their mind (15%) or because of his age (15%).

As other polls have found nationally, health care is the most important issue that would affect vote (29%) followed by climate change (18%). Similarly, when asked to rate the importance of a nominee's support for certain issues, taxing the very wealthy comes out on top (64% call it very important), followed by Medicare for all (57%). Fewer prioritized impeaching President Donald Trump (41% very important), free higher education (39%) or breaking up big tech companies (26%).

Three-in-five likely Democratic caucus participants said it was more important to nominate a candidate who can defeat Trump over someone who reflects their priorities (34% preferred a candidate who reflects their priorities), another finding similar to the national population.

Regardless of how they intend to vote, Democrats and Democratic-leaning independents nationally think Biden would be the best leader and has the best chance of beating Trump in the Quinnipiac poll. But the proportion who think Biden would be the best leader is down from 44% in April to 26% now.

When asked which candidate had the best policy ideas, Warren won out with 31%.

The USA Today/Suffolk University poll of likely Democratic caucusgoers in Iowa was conducted by telephone June 28 through July 1 among a random sample of 500 likely caucus participants. Results among the full sample have a margin of sampling error of plus or minus 4.4 percentage points.

The Quinnipiac University poll of Democrats and Democratic-leaning independents was conducted by telephone June 28 through July 1 among a random sample of 554 registered voters. Results among the Democratic sample have a margin of sampling error of plus or minus 5.0 percentage points.