Consider the following questions:
But if the House sits on the impeachment articles, then what will give them enhanced subpoena powers?
The only practical basis on which impeachment would give the House enhanced subpoena powers would be during the trial in the Senate. And really, that would mostly consist of having the Chief Justice preside over the trial, since the only body that could over rule the Chief Justice would be the Supreme Court. So the Chief Justice would rule and the Supreme Court would review. This might well drop out additional stages of review, like the circuit courts.
As is, the subpoenas would be fought in a regular district court, appealed to a circuit court, then to en banc review, and finally to the Supreme Court. But my point is that sitting on articles of impeachment doesn't get past that for them. They would actually have to prosecute the impeachment.
What would stop Donald Trump or people speaking for him from saying, "Well, if they were so sure that he deserves impeaching, why don't they send the articles of impeachment to the Senate?"
Again, an unfinished impeachment is a failed impeachment in effect. It leaves Trump in office and able to accuse them of a witch hunt. Proof? If it weren't a witch hunt, they'd impeach him and present the evidence to the American people. Since they aren't doing that, obviously they don't have the evidence. They are simply playing political games.
Supporters of impeachment will disagree. But until Republicans start becoming supporters of impeachment, that won't matter. It would take twenty Republicans in the Senate to vote to convict to actually remove Trump from office. And that's assuming that Joe Manchin and Angus King vote to convict.
So even if they could sit on the articles of impeachment, what would they gain? They'll have taken a partisan vote for no effect. This will annoy Trump supporters and some people on the fence about Trump. And it only highlights the fact that the Democrats could impeach but were not doing so to Trump opponents. Who then may see no reason in voting against Trump and for Democratic candidates. So Democrats might lose the House and see Trump re-elected. Which is of course the argument against impeaching at all.
One comment suggests that impeaching would make the administration more willing to provide evidence. But I think that the reverse would happen. If the administration thinks that giving the House more information increases its actual legal jeopardy, it will stonewall even more. Trump might win an impeachment trial now. If he gives more information that Democrats can use against him, he might lose. So I would expect him to resist even more strongly as the threat rises.
Another point is that while trying an impeachment may make the subpoena powers quicker, it also makes them narrower. Right now the House may subpoena anything it wants. The restrictions will be based on their legal authority to investigate. In a trial, subpoenas are restricted to information relevant to the trial. So if they want, for example, Trump's tax returns, they would have to link the tax returns to the impeachment charge. It's not immediately clear to me that John Roberts (the Chief Justice) will interpret that expansively.
It would be quite natural to say that tax returns have nothing to do with obstructing justice. It would also be quite natural to say that the president has some form of privilege when communicating with lawyers in his employ.
Another problem is that if they impeach and fail, it would be hard to impeach later if they found better charges. Because the Republicans will have mostly chosen their sides at that point and there is little political value in switching.
If Republican voters think that Trump is innocent, then Republican politicians who vote to impeach are likely to lose their primaries. Thus Republican politicians really need voters to be at least willing to believe the charges before they can vote to convict on them. Now, a successful impeachment is likely to shift some voters' minds. So it doesn't necessarily need to be a majority saying to impeach. But they need there not to be a clear majority against impeachment.
They also have the problems of
Establishing an underlying crime for which Trump is obstructing justice. As is, the main charge is that he was obstructing the Russia investigations. But he was exonerated of crimes in that investigation. They would want to charge him with this crime as part of the impeachment.
Establishing that he was overreaching his authority. There's an argument that Trump couldn't obstruct justice by firing Comey because Trump had the right to fire Comey. That it was improper for Comey to investigate Trump after the inauguration because that oversight power is held by Congress. It is Congress that should have been investigating Trump, not Comey and the FBI.
Establishing that the reason Trump took various acts (like firing Comey) was to obstruct the investigation. If Trump says that he fired Comey because Comey's too tall, that's not obstruction of justice.
They certainly haven't established an underlying crime. Trump was specifically exonerated on the charge that Mueller was investigating. This may be enough for some Republican Senators to vote against impeachment in and of itself.
The argument that he was within his rights is a bit of a problem regardless. Republican Senators will have to think long and hard about precedents around that as well as the impact on their own careers (voting for impeachment reduces their support among Republicans without necessarily increasing their support among Democrats and independents).
For most Democrats, saying "I don't believe Trump" is cheap. They can say that with no electoral harm. For Republicans, saying "I don't believe Trump" could subject them to a primary challenge or weaken their results in the general (from a lack of turnout by the base).
How this will play out politically is hard to guess. There haven't been enough presidential impeachments to set a pattern. The more recent one strengthened the president after his party was near unanimous in standing with him. That's the Democrats' number one fear. If they don't have enough votes, trying and failing may actually strengthen Trump, as it did Clinton.
In the one case where an impeachment threat led to the president leaving office (Richard Nixon), he resigned. So we don't know how the trial would have played out. After impeachment, Trump could be like Clinton and end up stronger. Or like Nixon with almost everyone convinced of his guilt. Or he could be like Andrew Johnson and skate through.