WASHINGTON — Lawmakers negotiated Tuesday over a final batch of President Obama’s judicial nominees with Democrats hoping to win Senate confirmation for up to a dozen of them, a final burst that would push this year’s total to the highest annual figure in 20 years.

The Senate has approved 76 federal court of appeals and district court judges so far this year. Confirmation of 12 more would bring this year’s total to 88 — the most since a Democratic-led Senate approved 99 of President Bill Clinton’s appeals and district court nominees in 1994, according to Russell Wheeler, who studies the judiciary at the Brookings Institution.

Whatever this year’s figure, it will easily surpass the 43 approved last year and the 49 confirmed in 2012. Majority Democrats enabled that in November 2013, when they muscled through a weakening of the Senate’s rules on filibusters, the procedural delays that minority parties have long used to sink nominations and bills they dislike.

“Republicans have just slow-walked judicial nominations,” said Sen. Tom Harkin, D-Iowa. “What we’re doing is what we should have done the last couple of years.”

Senate leaders were hoping to end this year’s session as soon as Tuesday night. Thanks to their triumph in last month’s midterm elections, Republicans will run the Senate in next year’s Congress — and are sure to slow the pace of approving Obama nominees.

Lawmakers from both parties said discussions between the two sides were underway to see how many of Obama’s judicial picks the Senate would approve before adjourning.

Several lawmakers said Democrats got a chance to consider more nominees than expected after conservatives led by Sen. Ted Cruz, R-Texas, forced a vote last weekend on Obama’s executive actions deferring the deportation of millions of immigrants. They said that gave Reid more time to hold votes on nominations.

Senate Minority Leader Mitch McConnell, R-Ky., declined Tuesday to discuss last weekend’s events with reporters, saying, “We are where we are, and I’m hoping we’ll wrap it up today or tomorrow.”

Two senators said that at a closed-door lunch Tuesday for GOP senators Cruz offered an apology if his effort had forced any lawmakers to change their Christmas break plans. He did not specifically express regrets for opening the door to Senate approval of more nominees, said the lawmakers, who agreed to describe Cruz’s remarks only on condition of anonymity.

Cruz spokeswoman Catherine Frazier said the lawmaker apologized to colleagues for inconveniencing their personal schedules. She said his goal was to force a vote on Obama’s “illegal” immigration actions.

The 88 judges would mean the Senate would have confirmed 303 federal appeals and district court judges through Obama’s six years in office, according to Wheeler. That would be more than the 298 confirmed during Clinton’s first six years and the 253 confirmed during that same period under President George W. Bush.

Such numbers will let Obama put his imprint on the federal judiciary, though judges don’t always follow the political ideology of the president who picked them.

Currently, there are 50 federal appeals and district court vacancies out of 856 judgeships, according to data from the U.S. court system. That’s the lowest number of vacancies since December 2008, the month before Obama took office. Vacancies during his presidency peaked at 108 in December 2010.

Of Obama’s judges confirmed so far, 42 percent have been women, 19 percent black and 11 percent Hispanic, the White House said. That exceeded the percentages of his immediate predecessors, Bush and Clinton, the White House said.

Another measure of Obama’s impact is on federal appeals courts, which have enormous influence on their regions of the country and can be conduits for cases to reach the Supreme Court. When he took office, 10 of the 13 appeals courts had more judges appointed by Republican than Democratic presidents. Now the balance has switched, with Democratic-appointed majorities on nine of the courts.

Most significantly, that includes the federal appeals court for the District of Columbia circuit, considered the nation’s second-most powerful court because its jurisdiction includes actions by the White House and federal agencies.