The Oakland Police Department, with help from the FBI, is investigating both displays as possible hate crimes.
The Equal Justice Initiative documented racial terror lynchings during the post-emancipation Reconstruction era, from 1865 to 1876.
Sen. Cory Booker made an emotional plea for the Kentucky Republican to yield his objections.
The pioneering Black journalist is revered for her reporting that exposed lynching as a white tool of political terror against Black people.
The bill, which was named after Till, comes 120 years after Congress first considered anti-lynching legislation and after dozens of similar efforts were defeated.
"The impeachment inquiry is not a lynching. Don't believe me? Ask your Klan-ass dad."
Several other Democrats also used the term in reference to the former president's impeachment in 1998.
The Senate majority leader offered mild disapproval of the president's offensive attack on the impeachment process.
"The story here is not the word, it’s the conduct of the Democrats in the House,” the South Carolina senator said.