He said the firing of Comey opened the floodgates surrounding this scandal, and many Republican leaders have to be now thinking about the broader damage to the party in 2018 and beyond, referring to the mid-term elections next year.

"Unless they are able to completely change the course of this crisis - perhaps by setting up an independent investigation and getting everything out in the open - the Trump policy agenda, and many key GOP goals, are on life support," Mahaffee said.

Darrell West, vice president and director of governance studies of the Brookings Institution, told Xinhua the controversy is "a major setback for Trump's policy agenda."

Indeed, Trump was elected in large part as an agent that could rejuvenate an economy that has still not fully recovered from the 2007-2008 economic disaster. Now experts said the dust-up could distract him from his policy agenda.

"Instead of discussing tax reform and healthcare repeal, leaders are focused on the Russia investigation and whether Trump obstructed justice in this case," West said.

The whole situation has taken the president and congressional leaders off-message and forced them to explain what the ties were between Trump's staff and Russia, he said.

Republicans have criticized Trump for his actions on Comey, but have not been very forceful at pushing an investigation. They are worried about Trump's declining poll numbers, but most Republican legislators have been pretty muted in their comments.

"They are waiting to see what gets uncovered and how much trouble the president is in," West added.