Why hasn't Congress pressed their subpoenas in court, and if they have, why have they been ineffective at getting witnesses from the White House to come forward?
They shouldn't have to1 (18 U.S. Code § 1505), and, when they try, it gets into a drawn out battle in the courts. So they take the position that failure or refusal to respond to a subpoena is obstruction of Congress.
INVOKING NIXON, PELOSI AND SCHIFF WARN TRUMP THAT FURTHER STONEWALLING IS GROUNDS FOR OBSTRUCTION OF CONGRESS, 10/2/19.
House Speaker Nancy Pelosi (D-Calif.) and House Intelligence Committee Chairman Adam Schiff (D-Calif.), the Democrat now leading the chamber's impeachment inquiry, warned President Donald Trump Wednesday that any attempts to further stonewall their congressional investigations will result in obstruction of Congress—a charge that former President Richard Nixon faced as one of his articles of impeachment.
"Any efforts by [Secretary of State Mike Pompeo], by the president or anyone else to interfere with the Congress' ability to call before it relative witnesses will be considered evidence of obstruction of the lawful functions of Congress," Schiff said. "Of course, that was an article of impeachment against Nixon."
18 U.S. Code § 1505. Obstruction of proceedings before departments, agencies, and committees
Whoever corruptly, or by threats or force, or by any threatening letter or communication influences, obstructs, or impedes or endeavors to influence, obstruct, or impede the due and proper administration of the law under which any pending proceeding is being had before any department or agency of the United States, or the due and proper exercise of the power of inquiry under which any inquiry or investigation is being had by either House, or any committee of either House or any joint committee of the Congress--
18 U.S. Code § 1515. Definitions for certain provisions; general provision
(b) As used in section 1505, the term “corruptly” means acting with an improper purpose, personally or by influencing another, including making a false or misleading statement, or withholding, concealing, altering, or destroying a document or other information.
1 Concerning They shouldn't have to in its reference to Why hasn't Congress pressed their subpoenas in court.
Congress believes they shouldn't have to go to court because the law is settled and allows them to issue subpoenas to compel the attendance and testimony of witness and delivery of documents.
Article I, Section 9, Clause 18.
To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.
Congress enacted laws under a due Constitutional authority. Any obligation to support to Constitution of the United States includes respecting such laws. The entirety of "18 U.S. Code CHAPTER 73—OBSTRUCTION OF JUSTICE" (as amended) including "18 U.S. Code § 1505. Obstruction of proceedings before departments, agencies, and committees" (as amended) were duly enacted by Congress and signed into law by presidents.
It is clear that failure to appear in response to a subpoena violates the law and fails to support the Constitution, an obligation of executive officers. See Article VI, Clause 3.
But, what is one believes the investigation is not due and proper? Then one appears in answer to the subpoena, and refuses to answer questions "on the advice of counsel" and setting forth the reason, or similar.
The Court has long since accorded its agreement with Congress that the investigatory power is so essential to the legislative function as to be implied from the general vesting of legislative power in Congress. “We are of the opinion,” wrote Justice Van Devanter for a unanimous Court, “that the power of inquiry—with process to enforce it—is an essential and appropriate auxiliary to the legislative function. . . . A legislative body cannot legislate wisely or effectively in the absence of information respecting the conditions which the legislation is intended to affect or change; and where the legislative body does not itself possess the requisite information—which not infrequently is true—recourse must be had to others who possess it. Experience has taught that mere requests for such information often are unavailing, and also that information which is volunteered is not always accurate or complete; so some means of compulsion are essential to obtain what is needed. ...
It has long been settled that the courts may not intervene directly to restrain the carrying out of an investigation or the manner of an investigation, and that a witness who believes the inquiry to be illegal or otherwise invalid in order to raise the issue must place himself in contempt and raise his beliefs as affirmative defenses on his criminal prosecution. This understanding was sharply reinforced when the Court held that the speech-or-debate clause utterly foreclosed judicial interference with the conduct of a congressional investigation, through review of the propriety of subpoenas or otherwise. It is only with regard to the trial of contempts that the courts may review the carrying out of congressional investigations and may impose constitutional and other constraints. [Emphasis added.]
All the president’s privileges, December 19, 2019.
District Court Judge John Bates rejected Miers’ claim of immunity, holding that she was required to appear and give testimony, although Bates did note that executive privilege might support refusals to respond to particular questions. Judge Jackson largely endorsed the reasoning of Judge Bates in justifying her decision. The Miers case did not, however, settle the law, even for the District of Columbia (the district in which her case was heard). Although Judge Bates’ opinion is detailed and thoughtful, it was never reviewed on the merits by a higher court because the appellate process was unlikely to be finished before the expiration of the 110th Congress, at which point the committee’s subpoena would lapse. [Emphasis added.]
However, when one is face with conflicting orders, one could use the Kupperman defense.
In rare unity, Trump and House Democrats want the same outcome in impeachment subpoena case, DECEMBER 10, 2019.
Lawyers for House Democrats and President Trump were back in federal court on Tuesday. But this time, they were arguing for the same outcome: They want a lawsuit filed against them to be thrown out.
Charles Kupperman, Mr. Trump's former deputy national security adviser, sued both parties in October after he was subpoenaed by the House to testify in the impeachment inquiry but ordered by the White House not to appear.
The White House claims that the president's senior officials have "absolute immunity" from congressional subpoenas. That stance led more than a dozen current or former Trump officials to refuse subpoenas related to the impeachment process of the president.
House Democrats, however, withdrew their demand for his testimony last month, citing the length of time it would take to litigate the case. Without Kupperman's testimony, the House started the formal impeachment process on Tuesday, after weeks of hearings with more than a dozen other witnesses. In court, House lawyers said Democrats will neither hold Kupperman in contempt nor attempt to subpoena him again.