Coming from this Congress a censure would almost be a badge of honor, so why would he give into the demands? The only reason I can think of is he would lose his standing on powerful committees, Any others?
“Presumably, censure of the President would take the form of a resolution adopted by both the House and Senate and then publicly announced. Legally, the resolution would have no effect. Censure derives from the formal condemnation by either the House or the Senate in rebuke of a Member of their own body. After a majority vote, the Member is publicly denounced, but still retains the position of Representative or Senator. However, the House removes the offending Member from any leadership positions in committees or sub-committees.”
http://www.winwithoutwarus.org/html/new_censure.whatis.html#whatis‘Today Stark is the longest-serving member of Congress from California. He has been a ranking member of the Banking and Currency Committee and powerful Ways and Means Committee. His voting record is generally very liberal, as indicated in the ratings section below, and he has been voted the most liberal member of Congress for two consecutive years. He was a founding member of the Congressional Progressive Caucus.
Stark is known to have a longstanding interest in health care issues and has been critical of the fate of the uninsured under the current administration.<4>’
http://en.wikipedia.org/wiki/Pete_Stark