So, technically the Senate can't stop the House from moving forward with the impeachment process steps. It can, however, stop a president from being convicted and removed from office. In fact, in several instances throughout history, American presidents have been impeached by the House, but not convicted by the Senate meaning they remained in office.
Remember this: Republicans control 53 seats in the Senate. Even if the Democratic-led House impeaches Trump, he will not be removed until 67 senators vote to convict him. Which, by a bit of back-of-the-envelope math, means that 20 GOP senators would have to side with all 47 Democrats (and independents who caucus with Democrats) in the Senate for Trump to actually be removed.
A simple majority of the House of Representatives (at least 218 votes) is required to impeach a U.S. President followed by a two-thirds majority vote in the Senate (at least 67 votes).
