WASHINGTON — Senator Kyrsten Sinema, Democrat of Arizona and one of her party’s only holdouts on President Biden’s sprawling budget bill, has cultivated a profile in Congress as a business-minded centrist.

But her refusal to raise tax rates on high earners and major corporations to pay for Mr. Biden’s plan is pushing Democrats toward wealth taxation and other measures once embraced only by the party’s left flank.

The frenzied search for new paths around Ms. Sinema’s tax-rate blockade has cheered liberals but raised serious qualms among more moderate Democrats, who now openly say they hope that Ms. Sinema’s business allies will pressure her to relent once they — and she — see the details of the alternatives that she is forcing on her colleagues to pay for around $2 trillion in spending on social programs and anti-climate change initiatives.