A group of Trump allies in the House of Representatives officially made their move to impeach the official who set up the special counsel investigation and whose firing could blunt or end it.

They claim the grounds for impeachment of Deputy Attorney General Rod J. Rosenstein is his alleged stonewalling of their document requests into investigations into Justice investigations of Hillary Clinton and President Trump.

But that gets harder to believe when you look at this group’s penchant for using the “i-word” against their political opponents, their Republican colleagues' lack of support for impeaching Rosenstein and all the reasons to believe there is a GOP conspiracy to help Trump undermine the independent Russia investigation.

They don't even have the support of House Speaker Paul D. Ryan (R-Wis.), who slammed down the notion this impeachment case is legitimate less than 24 hours after it was filed. "I don't think we should be cavalier with this process or this term," he told reporters of impeachment. "Number two, I don't think this rises to the level of high crimes and misdemeanors, which is a really high standard."

Let’s start with the house of cards this impeachment case seems to be built upon. House Republicans have been entangled in a back and forth with the Justice Department for months over access to classified FBI documents. The Justice Department essentially says it's trying to comply, but that these Republicans want a lot, and it takes time.

The Washington Post reports the FBI says it had to write a new software code to look up the documents Republicans want.

One Republican, House Oversight and Government Reform Committee Chairman Trey Gowdy (R-S.C.), said he thinks the department is coming around on document requests. "If you see the votes in the jury, let me know," Gowdy told The Post's Mike DeBonis of the likelihood of impeachment proceedings. "I don't see the votes." Gowdy, we should note, is no shrinking violet when it comes to challenging the executive branch.

Also,  it takes a lot of imagination to believe that slowness or resistance to document production in the federal government is the result of an anti-Congress conspiracy that is directed all the way from the top.

“When you find some problem with production and questions, it doesn't mean I'm personally concealing something from you,” Rosenstein replied when Rep. Jim Jordan (R-Ohio), one of the impeachment articles's authors — who just announced he's running for speaker after Ryan leaves this year — accused him of hiding information. “It means we are running an organization that is trying to follow the rules.”

House Republicans have also used impeachment as a political tool before — including against IRS Commissioner John Koskinen, whose agency focused on conservative groups for extra scrutiny.

Put another way, it seems more possible that instead of rooting out some secret government conspiracy to hide documents, these conservatives' frustration over access is rooted more in normal tension between information sharing between the executive and legislative branch. Especially when it comes to classified information, which Congress doesn’t automatically own the rights to use.

If the case for impeaching Rosenstein is flimsy, the case that this impeachment drive is rooted in ending the Russia investigation is much stronger.

Some of this group’s allies have threatened to impeach Rosenstein before if he didn’t give them another set of documents. Those got handed over, but it established a trend.

Here's House Intelligence Committee Chairman Devin Nunes (R-Calif.) in April:

Nunes did not sign onto the impeachment articles, but he has been a key player in much of the tension between the Russia investigation and Trump's allies in Congress.

Republicans have also taken the FBI agent Peter Strzok affair texts out of context, and released a discredited memo alleging FBI bias in the beginning of the Russia investigation that Trump considered using to fire Rosenstein. These lawmakers, much like the president, have generally seemed willing to jump on anything that makes the independent Russia investigation look bad.

We already know making the Russia investigation and people around it look bad is one of Trump's main objectives. He tries to do it on a daily basis. If he wanted to end it without, say, causing a constitutional crisis that firing the special counsel might, getting rid of Rosenstein is the way to do it. Trump could simply put someone else in his place who was more inclined to blunt or hamper the investigation.

Given the shaky lines in this impeachment move and the much starker ones between some Republicans’ actions and Trump’s desire to undermine the Russia investigation, it seems likely that House Republicans just made their boldest move yet to impede or end the Russia investigation.