House Democrats gave themselves political wiggle room when they launched their impeachment inquiry without holding a floor vote, but that procedural strategy also left room for the White House and a federal judge to question the legitimacy of the push.

The White House, in a letter Tuesday criticized as advancing a legally flimsy argument, told the House it would not participate in an impeachment inquiry that hasn’t been authorized by the full House — which they argue means it isn’t “a valid impeachment proceeding.”

[Judge questions keeping Mueller grand jury materials from House]

And a federal judge, hearing arguments Tuesday about whether the House Judiciary Committee should get grand jury materials from the special counsel report from Robert S. Mueller III as part of an impeachment inquiry, questioned when she could know such an inquiry had begun if there wasn’t a floor vote.

“Where are you suggesting I should draw lines?” Chief U.S. District Judge Beryl A. Howell asked House General Counsel Douglas Letter.