WASHINGTON — Senate Democrats plan to force a vote this week to fill a vacancy on the court widely considered the country’s second highest, threatening to reopen the bitter fight over limiting the filibuster if Republicans follow through on their pledge to block the nomination.

Unless one party backs down, the battle could escalate into a reprise of the partisan strife that paralyzed the Senate for several weeks over the summer. But this time the long-term implications could be far greater, both for the Senate as an institution and for the ability of any president to shape the ideological bent of the federal bench.

At the heart of the dispute are lifetime appointments to the United States Court of Appeals for the District of Columbia Circuit, which often renders judgments on whether a president’s policies are constitutional. The future of the Supreme Court is also a factor: Judges who sit on the circuit court have been elevated to the Supreme Court four times in the past 30 years.

Given that President Obama could have another Supreme Court vacancy to fill before his second term ends, any fight now over judicial nominees takes on added weight.