George Bush' Republican party took that control away from the Dems in Bill Clinton's first term.
Please don't try to confound "Ronald Reagan" and "Republican party". There are different ambitions and capacities involved. Ronaldus Magnus was taking on the world when the Republicans were still cowering in the Capitol basement bemoaning their fate.
Ronaldus did business with Tip O'Neil because he had too, but Tip O'Neil did business with Ronaldus because he respected him and his ideas.
History revisionism!!
The Democrats had control of the Senate and the House for 40 years. Hillary Clinton's health plan and Newt Gingrich's GOP Contract With America gave the GOP control of the Senate and House in 1994. Then GWB, Karl Rove and Ken Mehlman gave back control of Congress to the Democrats.