Will Congress investigate Trump after he leaves office?

More from House Speaker Nancy Pelosi, including how she intends to use the Democrats' new majority in Congress.

Will the House continue to investigate Trump?
Will the House continue to investigate Trump?... 02:55

On Tuesday, Democrats won both Senate seats in Georgia's runoff election, giving them a narrow majority in the next Senate, with the help of potential tie-breaking votes from Vice President-elect Kamala Harris. Having also defended their majority in the House of Representatives last November, the Democrats will have control of both chambers of Congress — as well as the presidency — come January 20.  

But the events in the 24 hours that followed — an insurrection, instigated by the president, that led to the death of five people — largely overshadowed the news.  

In a wide-ranging interview this week with House Speaker Nancy Pelosi, correspondent Lesley Stahl asked about the Democratic Party's new majority in Congress and how the Speaker intends to use it.  

WILL THE HOUSE CONTINUE TO INVESTIGATE TRUMP?

The talk on Capitol Hill currently centers on what action politicians will against President Trump before Inauguration Day. Will the House vote to impeach him? Will the cabinet invoke the 25th Amendment?  

But the questions of how to handle Mr. Trump's involvement in Wednesday's mob do not expire when his term does at noon on January 20. Will the House continue to investigate him after he leaves office? 

"We'll see," Speaker Pelosi said. "It's not a question of let it go. We're not going to let go an insurrection in our country and the attempt of coup d'état so that we cannot validate the election of the next president of the United States." 

The Speaker said she has told her members to see what opportunity exists and assess what it will accomplish. She also said the House will continue pursuing cases already underway, including the subpoenas they have already issued. 

Speaker Pelosi pointed out that, with regards to potentially illegal activity, those who have surrounded the president could also be exposed.  

"Do we want to get on with the future? Yes, of course," Speaker Pelosi said. "But it doesn't mean that we cannot bring justice to the system as we do so." 

POLICY ISSUES & USING RECONCILIATION

Speaker Pelosi on the Democrats' new majority... 03:58

Now that Democrats are set to control both the House and Senate, Speaker Pelosi is looking ahead to policy priorities she thinks her party will be able to pass, including lowering the cost of prescription drugs and rebuilding American infrastructure.  

"We have an array of issues, of legislation, that have been sitting over on Mitch McConnell's desk that passed in a bipartisan way in the House but that he would not bring up" Speaker Pelosi said. "So the power of bringing up legislation makes a big difference." 

There are also bills the Senate can now pass without needing any Republican votes, through a legislative process known as reconciliation. Budget reconciliation applies to certain tax, spending, and debt legislation and allows the bills to pass in the Senate with a simple majority, which the Democrats will have. Most other legislation requires a majority of 60 Senate votes and provides senators with the ability to use the filibuster to indefinitely prevent a bill's consideration. The Democrats passed the Affordable Care Act in 2010 through reconciliation.  

"Georgia was like winning ten votes from the standpoint of reconciliation," Speaker Pelosi told 60 Minutes. 

THE RUSSIA HACK AND TRUMP'S TAXES

Speaker Pelosi on getting Trump's taxes 03:37

One of the subpoenas the House is pursuing involves President Trump's tax returns, which Speaker Pelosi said may reveal the extent of the president's ties with Russia.  

This week, top national security agencies confirmed that Russia was likely responsible for a vast hack of U.S. government departments, contradicting Mr. Trump's unsupported claim that China was potentially to blame. Speaker Pelosi said that, rather than asserting authority over Russia, Mr. Trump was instead a "handmaiden" for Russian President Vladimir Putin. 

The Speaker also said she agrees with Sen. Mitt Romney, who said the cyberattack amounted to an invasion.   

"We have to go forward to make sure we have the proper protection in terms of cybersecurity for our country because this was a very major assault," she said. 

The Speaker said she has not received a full briefing on what happened and said the intelligence community may not have the full picture yet.   

"But what we do know is the president is, once again, in his Putin denial," the Speaker said. "What is it that Putin has on him?"

To watch Lesley Stahl's 60 Minutes interview with Speaker Pelosi, click here. 

The videos above were edited by Will Croxton.