Former House Oversight Committee Chairman Trey Gowdy, R-S.C., said Wednesday that House Oversight Committee Chairman Adam Schiff, D-Calif., is trying to force the U.S. Senate to make the impeachment case he failed to build in the House.

Gowdy said on "The Story" that Schiff had the opportunity to go through the legal process and subpoena administration figures he considers "key" to the impeachment case -- including former National Security Adviser John Bolton.

"It is tough and it is time-consuming to run real investigations," Gowdy told host Martha MacCallum. "I got a lot of criticism for the two years I took trying to get documents and information from the Obama Administration, but unfortunately, that is the way the system works."

Gowdy added that Schiff appears to hope the U.S. Senate is "dumb enough" to let him off the hook in that regard.

"What Schiff decided was: 'I'm not going to call Bolton, I'm not going to call Mulvaney or Pompeo. I'm not even going to send a subpoena to them. I'm going to wait until it gets to the Senate and then if the Republican senators are dumb enough -- and they're not -- but if they're dumb enough to do what I would not do, we can all hear for the first time whatever this evidence is," he said.

Gowdy also said that instead of building a comprehensive case with the witnesses and documents Democrats wanted, Schiff rushed his case along an "artificial timeline" that ended before Christmas.

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During his remarks on the Senate floor, Schiff claimed President Trump has acted in a way that the Founding Fathers had "feared," and pressed for the Senate to consider all witnesses and documents he deems relevant. However, Schiff also has rejected calls by Republicans to subpoena Hunter Biden -- who did business in Ukraine.

Gowdy added that Schiff's actions -- or inaction -- may have intentionally left Republican Sens. Cory Gardner of Colorado, Thom Tillis of North Carolina and Martha McSally of Arizona facing "difficult votes" on calling the aforementioned witnesses, as their seats are in danger of flipping blue in November.