Democrats have thrown a spotlight this week on a centuries-old tool to give senators in the minority party the power to block bills — and many are pushing to change or end the practice as they prepare to shepherd a liberal agenda through a sharply divided Senate.

The filibuster, which creates a 60-vote hurdle that many measures must clear in order to pass the upper chamber, could paralyze the Biden administration’s agenda by requiring Democrats to persuade at least eight Republicans to support virtually every bill of significance. With a major piece of voting reform legislation on its way to the Senate after passing the House earlier this month, Democrats have assigned fresh urgency to a perennial discussion over discarding, or at least loosening, the rule.