WASHINGTON — The first, biggest, clearest sign of how President Obama will govern in the last two years of his presidency will be whether he decides to nominate Labor Secretary Tom Perez to take over the Justice Department.

Administration officials have not signaled who will be nominated to replace Attorney General Eric Holder since he announced his intention to step down earlier this year — and now after Tuesday’s Republican wave, the White House has dwindling time before the GOP takes control of the Senate.

Nominating Holder’s replacement will signal loudly — more than anything the president said in an hour-long news conference Wednesday where “compromise” appeared to be the word of the day — how aggressive the White House plans to be in the final two years of the Obama presidency. It will likely be the first big move Obama takes in the post-midterm landscape. Who will his nominee be, and when will the name be sent to the Senate?

Obama mostly brushed the question of the attorney general nomination aside this week, citing “a number of outstanding candidates” under consideration. “I’m confident that we’ll find somebody who is well-qualified, will elicit the confidence of the American people, will uphold their constitutional obligations and rule of law, and will get confirmed by the Senate,” he said.

Perez is the liberals’ pick, with Latinos — from the Congressional Hispanic Caucus to the National Hispanic Leadership Agenda — already outright endorsing him for attorney general. Perez has a strong base of support from the broader civil rights community from his time running the Civil Rights Division at the Justice Department, as well, and he’s got plenty of friends backing him in organized labor. On Monday, Perez will be addressing the annual dinner of the National Women’s Law Center, along with longtime Obama friend and Commerce Secretary Penny Pritzker. The speech will give Perez the chance to woo another main group of the liberal coalition — and he’ll be doing it with Pritzker at his side.

Picking Perez, and potentially sending him through the lame-duck session of the Senate, would be an aggressive, confrontational move — the Labor secretary is not popular at all with Republicans, particularly regarding his work on “disparate impact” enforcement of civil rights laws and regulations. The confirmation process for Perez’s current position was heated.

The alternative is more sedate: The administration could nominate someone like Solicitor General Don Verrilli, a former lawyer at Jenner & Block who has represented big corporate interests, as well as the government and pro bono clients — something that might be seen as a way of “compromising and being constructive,” as Obama discussed on Wednesday.

Outside potential changes to the criminal justice system — an increasingly bipartisan interest — liberal legislation is off the table over the next two years. Obama could make few more clear signs that he wants to empower the Justice Department to take the lead on cementing a liberal or progressive legacy for the administration than going with Perez.