Firstly, an impeachment inquiry does not need to be voted upon to start. That precedent was started by the Clinton investigation.Few details you need to understand.
First step to resignation is impeachment (starting impeachment process does not require any specific reason, traffic ticket may be good enough reason too) - The House needs to impeach, but Pelosi does not want to take a vote because she does not have necessary number of votes for impeachment to pass.
Second, even if minor miracle were to happen (Trump impeached in The House), then decision will go to The Senate that requires 66 votes for impeachment to pass and even if Senate will decide to take a vote on impeachment there are no votes.
However, even if major miracle were to happen too (Trump impeached in The Senate) - it is still not good enough reason for Trump to go.
Third, impeachment does not mean that politician is required to leave.
For politician to go one needs to lose popularity with the constituency that has elected said politician and in case of Trump so far it is not happening.
Bottom line, anti-Trump losers are just as they usually are - losers.
Second, the Senate has already turned on Trump since the Syria fiasco, and possibly before. It's no longer a miracle.
Impeachment does not mean he is requiem to leave, but if the Senate convicts, he IS required to leave. He probably has no honor so he will try to pull an Assad and stay.