Elizabeth Warren is gaining ground. But her path to the nomination is harder than you think.

Elizabeth Warren has become the flavor du jour in the Democratic presidential race on the back of two strong debate performances. But her polling numbers suggest passing former vice president Joe Biden will be a much harder task.

The senator from Massachusetts has risen as the progressive’s progressive, refusing to run away from controversial stances such as eliminating private health insurance in favor of a government-run Medicare-for-all system. That approach has endeared her to the party’s far-left wing, but it leaves many less leftist Democrats cold.

All the recent national polls show her support is heavily skewed to the party’s left wing. The early August Quinnipiac poll, for example, shows Warren leading among self-described “very liberal” voters with 40 percent support. She falls to second among somewhat liberal voters with only 20 percent and trails badly among moderates and conservatives, where she garners only 11 percent support. The mid-August Economist-YouGov survey shows a similar pattern, giving Warren 27 percent of liberals but only 12 percent of moderates.

This leaves Warren in a difficult place. She’s strong enough among progressives to be a contender, but the ideas she peddles makes it harder for her to attract support from other voters as their preferred candidates drop out.

A CBS News-YouGov survey from early June makes this crystal clear. That survey breaks Democratic voters into three ideological groups: very liberal, somewhat liberal and moderate/conservative. On issue after issue, only the very liberal group agrees with many of Warren’s key ideas. The other two are either split or oppose them — moderates and conservatives often strongly so.

Warren’s signature issue, eliminating private health-care insurance, is a case in point. The survey showed that very liberals agreed with her by only a 51-49 margin. Somewhat liberals disagree by a 68-32 margin, and moderates and conservatives disagree by a 70-30 margin. It’s reasonable to assume that Democrats who agree with her are already likely to be in her camp. That means the overwhelming majority who disagree with her are split among other candidates. It’s hard to see why most of those voters would choose Warren over Biden or any more moderate choice in the final stages of the race.

The same splits arise in other areas. The survey found that very liberal Democrats are most interested in hearing where a candidate stands on fighting climate change or protecting abortion rights. Moderate Democrats, however, were more interested in hearing about how a candidate would create jobs than any other issue. Nearly half of moderates also wanted to hear about how a candidate would lower taxes; only about a quarter of very liberal voters agreed.

Warren’s best hope would rely on knocking out Sen. Bernie Sanders (I-Vt.) early and then pulling from his supporters. But no national poll shows her leading Sanders by an appreciable margin. Sanders runs far behind Warren in the number of paid staff and in formal organization, but he has the largest and deepest base of small donors of any candidate. He can therefore afford to stay in the race so long as he can demonstrate to his fanatical donor base that he has a chance to win.

That won’t be too hard for him to show if Warren doesn’t beat him soundly in early races. Since Democrats award delegates proportionally, so long as Sanders exceeds the 15 percent threshold to win delegates and keep close to Warren, he has no reason to drop out. He can show the same dogged resolve he demonstrated against Hillary Clinton, staying in the race and piling up delegates in a three-way contest that guarantees no one will have the necessary majority to win on the first ballot. The 77-year-old will never have another shot to run: Why would he make way for Warren even if she narrowly bests him in the early contests?

Warren’s tactics so far have more in common with those of evangelical religious-right Republican candidates than with eventual nominees. Those men — Mike Huckabee, Rick Santorum and Sen. Ted Cruz (Tex.) — used strong support from a large party faction to win early knockouts of other candidates with broader-based support. But they each lost when the race winnowed down to the final stage because the factors that earned them support from the religious right alienated them from the party’s silent majority. Warren’s progressivism could be enough to propel her forward, but it looks just as likely to alienate the moderate voters she will ultimately need to become the nominee.

Warren is a formidable candidate with niche appeal. She will have to display far greater nimbleness and skill if she is to break out from the progressive world she thus far seems most comfortable residing in.