WASHINGTON — The Senate brought President Trump to the brink of acquittal on Friday of charges that he abused his power and obstructed Congress, as Republicans voted to block consideration of new witnesses and documents in his impeachment trial and shut down a final push by Democrats to bolster their case for the president’s removal.

In a nearly party-line vote after a bitter debate, Democrats failed to win support from the four Republicans they needed. With Mr. Trump’s acquittal virtually certain, the president’s allies rallied to his defense, though some conceded he was guilty of the central allegations against him.

The Democrats’ push for more witnesses and documents failed 49 to 51, with only two Republicans, Mitt Romney of Utah and Susan Collins of Maine, joining Democrats in favor. A vote on the verdict is planned for Wednesday.

As they approached the final stage of the third presidential impeachment proceeding in United States history, Democrats condemned the witness vote and said it would render Mr. Trump’s trial illegitimate and his acquittal meaningless.