Washington (CNN) A Democratic lawmaker on Thursday ratcheted up warnings to the Trump administration amid a growing standoff over subpoenas and oversight requests the White House says it will resist.

Rep. Gerry Connolly threatened jail time for White House officials who are declining to comply with congressional committees' efforts to conduct oversight of President Donald Trump's administration. It's the latest salvo in the escalating battle between the White House and congressional Democrats , who have scaled up their oversight requests following the conclusion of special counsel Robert Mueller's investigation.

Connolly, who sits on the Oversight Committee, told CNN's Wolf Blitzer on "The Situation Room," "We're going to resist, and if a subpoena is issued and you're told you must testify, we will back that up."

"And we will use any and all power in our command to make sure it's backed up -- whether that's a contempt citation, whether that's going to court and getting that citation enforced, whether it's fines, whether it's possible incarceration," the Virginia Democrat added. "We will go to the max to enforce the constitutional role of the legislative branch of government."