The first bill of impeachment of President Trump has been introduced this Congress by Rep. Brad Sherman of California, H Res. 13. The bill was referred to the House Judiciary Committee. The bill is based on a charge of obstruction of justice for firing FBI director Comey, and a few other actions.
The House is streamlined to give great power to the Speaker and the Committee chairs to kill or bury bills or to rapidly pass legislation and have quick votes to allow the majority to pass bills without much minority input. As readers are no doubt aware, Democrats comprise the majority in the House, and the Republicans are in the minority.
Committee Chair Jerrold (“Jerry”) Nadler could refer the bill to a subcommittee, which will decide whether to hold hearings or not. The subcommittee would hold hearings and then vote the bill of impeachment “out of subcommittee” to the full committee. The full committee could hold additional hearings or not, and Chairman Nadler could delay indefinitely or schedule a vote rapidly. The power is his. Nadler could also handle the impeachment matter at the full committee level without making a subcommittee referral.
I do not know the Speaker Pelosi/Nadler relationship, but I find it difficult to believe that he would go against her wishes in how his committee handles the matter in terms of voting the bill “out of committee”. He wants a bill of impeachment that his committee reports out to get favorable treatment by Speaker Pelosi on the House floor. It is not obvious whether Speaker Pelosi wants an impeachment vote. If the President were not removed, because of a failure to pass the measure, public opinion would likely swing in favor of the President.
I believe that Rep. Jerry Nadler will probably support impeachment if he feels the case is strong enough, but I suspect he will want the Mueller investigation to finish and issue its report first. I also believe that Speaker Pelosi and Chairman Nadler want to try first to affect public opinion through a series of hearings in other committees concerning allegations of corruption and misconduct by the Administration.
Impeachment in the House requires a simple majority vote, which would follow the Judiciary Committee passing a resolution out of committee. It is somewhat likely but not definite that if a bill of impeachment makes it out of House Judiciary Committee, then it would pass the House. The biggest question facing Speaker Pelosi would be how those Democratic House members who come from swing districts would vote. They would face tremendous pressure from both sides.
The Senate is held by the Republicans, who comprise the majority in that chamber. Assuming the House voted to impeach, the Senate would then hold a trial of the President, with Chief Justice Roberts presiding, and conviction requires a two thirds vote of senators.
The Senate, in contrast to the House, gives considerable power to individual senators to slow down activity and stop appointments and bills from passing through amendments. (The votes confirming Justices Gorsuch and Kavanaugh follows a change in the rules of the Senate reducing the power of the minority or individual senators on those particular judicial appointments, but is not reflective of how the Senate usually works)
Unless public opinion among Republican voters shifts dramatically against President Trump in response to the Mueller findings or for some other reason, it strikes me as highly unlikely the Senate would convict President Trump to remove him from office based on what is currently publicly known and suspected.
This would be a replay of the Bill Clinton impeachment process, in which the House impeached him but the Senate did not convict.