I would be shocked if the White House fully complies, in which case the Senate Judiciary Committee has several options...negotiate with the WH which would likely drag out through the summer, find the WH in "contempt of congress", do nothing, or recommend an impeachment inquiry to the House.
In a similar scenario,thee WH is facing a deadline today on subpoenas issued earlier by the House Judiciary Committee on documents related to the firing of US Attorneys.
House Judiciary Committee Democrats warned yesterday they would pursue a contempt of Congress motion if the White House fails respond to subpoenas for testimony and documents related to the firings of U.S. attorneys last year.
The deadline for a response is Thursday, June 28. If the White House does not comply, it opens the possibility of a constitutional showdown between the two branches. In an ironic twist, the Department of Justice (DoJ) would be called on to enforce the contempt motion.
...
One of the contempt motions would likely be directed at Presidential Chief of Staff Josh Bolten, to whom the subpoena for documents was addressed, according to a Democratic aide.
Others who could face contempt motions include ex-White House Counsel Harriet Miers and former White House political director Sara Taylor. Last week, the House Judiciary Committee voted to subpoena testimony from Miers, while the Senate Judiciary panel voted to subpoena testimony from Taylor.
http://thehill.com/leading-the-news/...007-06-22.html
The WH may be gambling that they can win public opinion with the argument that the Dem Congress is pursuing these Oversight Investigations for purely political purposes.
IMO, this is mostly an "inside the beltway" issue....these WH/Congress confrontations on oversight differ from the confrontations on war funding and other higher priority legislative issues... and most voters may not give a shit about either side.