WASHINGTON—President Biden’s announcement last week that his administration would seek to forgive billions of dollars’ worth of federal student loans was cheered by progressives, the latest in a string of actions he has taken to shore up support from the left—annoying the center in the process.

       That has some Democrats worrying he is making a big mistake. Despite much recent hand-wringing about the unpopular president’s need to shore up his base with liberal appeals, polls show Biden’s principal weakness isn’t with the left but with the middle of the electorate. The president, some centrists argue, isn’t doing enough to appeal to the moderate and independent voters that tend to decide elections.

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