And while maintaining the six-vote margin is a constant worry for Republican leaders, the situation is going to get worse before it gets better.
Late last month, the House passed a budget measure much more to Mr. Clinton's liking by a bare six-vote margin.
But Republicans also know they must compromise to get important education legislation passed this year, especially in the House, where they hold a slim six-vote margin.
In the House, a bloc of liberal Democrats provided the tissue-thin six-vote margin to pass a budget very much like the one the President submitted last spring.
While she may well have committed political suicide, she became the darling of the House leadership by providing a critical vote for the budget bill, which passed with only a six-vote margin.
The House passed its version on May 27 by a six-vote margin.
Without the provision, the final bill could face trouble in the House, where the complete legislation passed by only a six-vote margin.
Yet because of the party's slim, six-vote margin, they are constantly the swing votes.
The House passed the measure by a six-vote margin.
The Senate passed the bill, 67 to 22, this afternoon and the House by a slim six-vote margin earlier this week.