I do not think they realistically thought this would accomplish to much, but it is a headline grabbing way to express their frustration at the apparent obstructionism.
"President Obama's attorney sent a letter to Congressional investigators on Friday, saying the White House would not cooperate with a subpoena requesting documents related to its doling out a $535 million loan guarantee to now bankrupt solar panel manufacturer Solyndra.
"I can only conclude that your decision to issue a subpoena, authorized by a party-line vote, was driven more by partisan politics than a legitimate effort to conduct a responsible investigation," Obama's counsel, Kathryn Ruemmler, wrote in a letter to the top Republicans on the House Energy and Commerce committee. (Read Ruemmler's full letter here)."
Head to the source for the link to the full response and to see the response to that response.