WASHINGTON » A fresh feud over federal judgeships has again begun to agitate the Senate, with Republicans so far blocking President Barack Obama from filling any of the four vacancies on the nation’s most prestigious and important appeals court.

After Republicans this week filibustered the nomination of Caitlin J. Halligan of New York to the U.S. Court of Appeals for the District of Columbia Circuit, Democrats quickly began discussions over how to respond. One possibility is for Obama to make several simultaneous nominations, in effect daring Republicans to find specific objections in multiple instances. Democrats say Republicans would be hard pressed to come up with legitimate reasons to disqualify all four.

"We need to design a strategy to counter the Republicans, and we are going to need the president," said Sen. Tom Udall, D-N.M. "Rather than putting just one up, we should put before the Senate all four and expose what is happening here."

Democrats say if Republicans were to continue to steadfastly block a series of appeals court nominees, Democrats might then have justification to revisit Senate rules and claim new power to thwart filibusters.

The District of Columbia appeals court is considered a route to the Supreme Court. In fact, Halligan was nominated to fill the vacancy left by Judge John G. Roberts Jr. when he left to join the Supreme Court in September 2005. The court decides many politically charged cases involving federal law and regulations, with one of its recent decisions overturning Obama’s recess appointments to the National Labor Relations Board.

The court currently consists of four judges appointed by Republican presidents and three appointed by President Bill Clinton, with four vacancies, the most ever on that court. Five of the six semiretired senior judges who share the workload were nominated by Republican presidents.

The filibuster of Halligan on Wednesday came just before the effort by Sen. Rand Paul, R-Ky., to block the nomination of John Brennan as director of central intelligence over drone policy. Paul’s old-school floor show was a media sensation. But the failure to end debate on Halligan’s nomination was arguably more consequential, given its potential to renew the fight over rules governing filibusters and how the Senate handles high-level judicial nominations.

Democrats believe Republicans are dead set against confirming qualified Obama administration nominees to federal circuit courts, especially the Washington appeals court, in order to preserve the current balance of power. They accuse Republicans of exaggerating their objections to Halligan to justify a filibuster under a 2005 agreement that averted the last partisan showdown over appointing judges.

That deal, crafted by what became the Gang of 14, a bipartisan group of senators, put its signatories on record as saying they would not block confirmation votes on appeals court judges without "extraordinary circumstances" as determined by each individual. While only members of the group signed it, the agreement became informal Senate policy and defused a crisis that had Republicans threatening to execute the "nuclear option" and bar filibusters against judicial nominees by a simple majority instead of the 67 votes historically needed to change Senate rules.

It also led to President George W. Bush’s winning three appointments to the District of Columbia court. All three appointees remain.

Overall, Obama has appointed roughly as many federal appellate judges as either Bush or Clinton did in each of their first terms. But Obama has appointed fewer federal judges to district courts, where trials are held, than Bush or Clinton in their first terms, partly because of Republican opposition and partly because of the administration’s own slowness to make nominations.

The appellate courts also have more vacancies today — 17 — than they did at the start of Bush’s second term, when 15 seats were open, according to Russell Wheeler, a Brookings Institution scholar who studies the federal courts.

In filibustering Halligan, several Republicans cited extraordinary circumstances arising from her work as the solicitor general for the state of New York, particularly on a case against gun manufacturers.

"Ms. Halligan advanced the novel legal theory that gun manufacturers, wholesalers and retailers contributed to a ‘public nuisance’ of illegal handguns in the state," said Sen. Charles E. Grassley of Iowa, the top Republican on the Judiciary Committee, accusing her of judicial activism. "Therefore, she argued, gun manufacturers should be liable for the criminal conduct of third parties."

Republicans also raised questions about the court’s caseload, saying the cost of adding another judge to the court was not justified by a backlog.

Democrats cried foul. Sen. Patrick J. Leahy of Vermont, chairman of the Judiciary Committee, called the claims on the workload disingenuous and said Republicans had resorted to smearing Halligan.

Democrats say that Halligan was acting in her official capacity representing the state of New York, not as a jurist, and that Republicans have abandoned the "extraordinary circumstances" test engineered by the Gang of 14.

"If you go back to that history of what occurred back then, there is a real question of whether they have broken the deal now," Udall said. "This is a key circuit for the country. What they are doing is not allowing these consensus candidate judges to get votes."

Udall has been among a group of relatively newer members of the Senate clamoring for significant changes in rules governing filibusters.

In January, working to avoid a divisive fight, Sen. Harry Reid of Nevada, the majority leader, and Sen. Mitch McConnell of Kentucky, the Republican leader, struck a deal making modest changes in the rules.

But those changes have done little so far to curb filibusters, as evidenced by the vote on Halligan and the obstacles raised to confirmation votes on Brennan and Chuck Hagel.

Hagel, a Republican former senator, found himself on the receiving end of a Republican filibuster before winning confirmation as secretary of defense.

Given the attention Paul received, the filibuster might even be enjoying resurgence as grand theater.

Democrats say that despite what they see as clear provocation, they are in no rush to change the new rules after just two months in place and while the parties are potentially making progress on other tough issues like immigration. They are more inclined to explore new ways to challenge Republicans over the vacancies.

The fight will take time. Democrats say they want to see how Republicans respond to future appeals court nominees, including another one to the District of Columbia circuit, Srikanth Srinivasan, Obama’s deputy solicitor general. But a series of filibusters against what they view as acceptable nominees could again bring to a head the push for a change in Senate rules.