Grand juries are a mysterious presence in our polity. Most people have a sense of what a trial is, but the function of the grand jury isn’t always appreciated.
A grand jury isn’t some sort of trial before the trial, making an initial finding of guilt or innocence. Rather it “is the function of the grand jury to determine whether the evidence presented in a specific case is sufficient to establish probable cause to believe that a crime was committed and that a specific individual committed the crime.”  “A finding of probable cause is proper only when the evidence presented to the grand jury, without any explanation being offered by the accused, persuades 12 or more grand jurors that a federal crime has probably been committed by the person accused.”  “The grand jury is not to weigh evidence to determine guilt or innocence.” 
For this reason, “exculpatory evidence will rarely be presented to a grand jury. Because the grand jury’s function is limited, the prosecutor has no duty to present evidence in his possession which tends to negate guilt….Further, an accused has no right to be called as a witness before the grand jury that is considering his or her indictment…, and he or she has ‘no right of cross-examination, or of introducing evidence to rebut the prosecutor’s presentation.’” 
The nation is now about to embark on President Trump’s Senate impeachment trial; and Senate Republicans have been saying that the House managers shouldn’t be allowed to allowed to call witnesses, but “should proceed with the evidence they used to impeach Trump in the House.”  Moreover, they have been echoing “the White House line that the House impeachment hearings violated Trump’s right to due process, despite the fact that the president refused to allow his lawyers to participate in those sessions.”  And now Senate majority Mitch McConnell has “unveiled ground rules on Monday for President Trump’s impeachment trial that would attempt to speed the proceeding along and refuse to admit the evidence against the president unearthed by the House without a separate vote.” 
It really is up to the Senate how it conducts its impeachment trials, and the argument cannot be made that impeachments should be handled exactly like indictments. But it is hard to make the case that impeachments, being quasi-criminal in nature, should be handled nothing like indictments.
The House of Representatives, having “the sole Power of Impeachment,”  stands in the place of a grand jury; the Senate, having “the sole Power to try all Impeachments,”  stands in the place of a trial court. Now it would be preposterous if a trial court refused to let the prosecution call any witnesses because it should have made its entire case in front of the grand jury; or limited the prosecution witnesses to only those who testified in front of the grand jury. The purpose of the impeachment hearings in the House wasn’t to obtain a conviction on the impeachment, but to form the impeachment charges. But Senate Republicans are claiming that the House should have gained testimony sufficient for a conviction before the Senate trial took place; and that while President Trump was obstructing its efforts.
If the Senate decides not to allow witnesses, there is nothing to be done. It has that power. But it should be known by all that the arguments for the Senate to act in that manner are utterly bogus, and outright disingenuous.