Thune's comments come as Trump is getting inaugurated on Jan. 20, with Trump planning to issue 10 executive orders on his first day in office.

No president has ever exercised this constitutional power, but "this remains a significant possibility in the eyes of the White House," one source said.

Thune sat down for an interview with the Washington Examiner that marked his first with a print outlet since assuming his new role as Senate majority leader.

Senate GOP leader John Thune (R-S.D.) is primed to hand President Trump a quick string of wins on his first days in office. Why it matters: Thune and Trump have a complicated history, but the new majority leader is doing his best to start Congress off on the right foot.

As for the fire-aid-for-debt-limit trade, GOP lawmakers who first raised the idea with Trump at recent Mar-a-Lago meetings said he was interested in the prospect at the time. That would mean making a debt limit hike part of a larger agreement around the bipartisan government funding talks.

With Donald Trump's agenda at stake, the top Republican leaders are divided on fundamental questions of strategy.

FIRST ON FOX: Senate Majority Leader John Thune, R-S.D., has selected four top Republican allies to be part of his unofficial cabinet as he looks to make his own impression on the upper chamber after taking the mantle from longtime GOP Leader Mitch McConnell, R-Ky.

President Donald Trump is expected to meet with House Speaker Mike Johnson and Senate Majority Leader John Thune on Tuesday. Multiple sources told ABC News that the meetings will happen separately on Trump's first full day in office.

Tuesday marks President Donald Trump's first full day in office. Keep up with the USA TODAY Network's coverage of his top priorities for Americans.

Hours after Trump was sworn in as president, senators confirmed his first Cabinet pick and advanced the nominations of several others through committee.

The Senate has passed a bill that would require federal authorities to detain migrants accused of theft and violent crimes.

The tactics are reminiscent of the ones taken the first time Trump entered the White House. At the time, Democrats homed in on eight nominees they would delay, with Senate Minority Leader Chuck Schumer (D-NY) warning against a “rushed” process.