This is a time of high anxiety for supporters of Hillary Clinton.

The polls show a tightening race between Clinton and a Republican nominee who, among other things, wants to date his own daughter, deport 11 million US residents and start a trade war with China.

Other polls show a close contest in the final Democratic primary in California, between Clinton and a challenger who, among other things, wants to raise taxes on everyone and is proud to call himself a socialist.

Since the only common factor in these two sets of troubling polls is Hillary Clinton, there must be a connection. Right?

Wrong. Let’s start with the Democratic race against Bernie Sanders, who shows no sign of throwing in the towel in this nomination battle.

The most recent polling last week, by the Public Policy Institute of California, shows that Clinton is leading Sanders by just two points, down from a seven-point lead in March.

But two days earlier, SurveyUSA released a poll showing Clinton ahead by 18 points. That was almost unchanged from a month earlier, when the same pollster put Clinton up by 19 points.

So Clinton may, or may not, be blowing her cake walk to the convention. But what if she is looking at the worst case scenario? What would a narrow victory, or even a defeat, mean for her campaign?

Not much in terms of the Democratic nomination: Clinton has such a commanding lead in pledged delegates and the popular vote – never mind the party’s super-delegates – that the identity of the ultimate nominee is clear.

A more serious question is the prospect of Clinton limping towards the finish line against a Republican nominee with a more consolidated party behind him.

To understand that scenario, it’s worth looking back to Barack Obama’s experience in 2008. Obama lost California by eight points to one Hillary Clinton, albeit at an earlier stage of the primaries, on Super Tuesday in February.

He also limped home to the nomination in the final three months of the campaign: a period the candidate liked to call the death march. Obama lost six of his last nine races, including Pennsylvania and Indiana: two states he would go on to win in the general election.

Sure enough, the least favorable poll for Clinton in California (by PPIC) also shows her beating Trump by 10 points. Moreover, it strongly points to a core weakness for Trump: around one third of Republicans are satisfied with their choice of presidential candidates, while just over half of Democrats say they are happy with their choice.

Still, the California polls also suggest that Clinton has several serious challenges of her own.

At the heart of Clinton’s troubles with Sanders are questions about her empathy, authenticity and honesty.

A YouGov poll for CBS News in April (giving Clinton a 12-point lead over Sanders), showed the former secretary of state in a dominant position over Sanders on questions of electability, effectiveness and policy.

However, Clinton trailed Sanders badly on questions of who was the more honest and trustworthy, as well as the most authentic candidate. Clinton’s poor ratings on trust and honesty were only underscored by last week’s highly critical report by the state department’s inspector general on her use of a private email server.

The one weak measure that she has a shot of overcoming relates to empathy. When asked ‘Which candidate understands people like you?’ in the YouGov poll, Clinton trails Sanders by 44 to 56 points.

This is a standard test where Democrats normally trounce Republicans: even John Kerry beat George W Bush on this question in 2004. Yet when translated to a contest against Trump, Clinton’s weakness is still evident.

In last week’s ABC News/Washington Post poll, which placed Trump ahead nationally (albeit within the margin of error), Clinton beats Trump on experience, temperament and having realistic policies. But when it comes to understanding voters problems and representing their values, she has only a single digit lead, within the margin of error, among registered voters.

Building a sense of empathy for voters – an emotional connection with working Americans – must be the Clinton campaign’s biggest priority as it re-introduces her to a skeptical public in the general election.

Failing that, the campaign is likely to revert to the path of least resistance: attack ads. Clinton and Trump are running equally poorly on issues of honesty and trust.

If it’s too late for Clinton to overcome her own problems with political expediency, at this late stage of a primary campaign and political career, she can at least drive home questions about her opponent.

Trump may enjoy a degree of authenticity now, but his own campaign has unfolded in ways that suggest the Clinton team will have ample fodder for attack ads. From his refusal to release his tax returns to his curious reluctance to reveal how much money he has raised for military veterans, Trump is a target-rich environment for questions about honesty and ethics.

Next week’s California primary will do nothing to change the outcome of this extended nomination contest.

But it has delayed the process of Democratic healing that Clinton clearly needs to lift her numbers and restore her party’s confidence. And it carries clear warning signs about the personal challenges she faces as she turns towards a national battle against an even less conventional opponent than a socialist from Vermont.