Yes and no
Yes, because the D's will gain resentment which will build into the next election. Party of No. This also may get Obama re-elected as historically happens.
No, because the R's want to stop the madness they see as madness via gridlock. They were put in to counteract the dems and gridlock achieves this.
In 2012 more D's are up for re-election in the Senate than R's. This will be key. If people believe that a R Senate and R House with a re-elected D can work...it just may, as it did for Clinton.