The statement came the day that news broke that Rudman, an influential budget hawk, had died on Monday.

Obama went on to say that Rudman represented the independence of the region he represented.

"Over almost 20 years representing the people of New Hampshire – first as Attorney General and then in the Senate – Warren was the embodiment of Yankee sensibility and New England independence," Obama continued. "As an early advocate for fiscal responsibility, he worked with Republicans and Democrats alike to call attention to our nation’s growing deficit.  And as we work together to address the fiscal challenges of our time, leaders on both sides of the aisle would be well served to follow Warren’s example of common-sense bipartisanship.  Michelle and I send our thoughts and prayers to the Rudman family."

Rudman's death came as legislators are seeking to avoid the "fiscal cliff" of automatic spending cuts and tax increases set to hit in January by hammering out a deficit-reduction plan. Rudman, while in the Senate, was most famous for his involvement in the Gramm-Rudman-Hollings Balanced Budget Act of 1985, which served as a model for the Budget Control Act of 2011.

In a separate statement released later on in the day Vice President Biden called Rudman one of the most knowledgeable legislators on budgetary matters in Washington D.C.

"Warren Rudman’s passion for public service was clear to anyone who met him. He was a tenacious prosecutor, a courageous combat infantry commander, and a devoted senator," Biden said. "He knew as much about the federal budget as anyone who ever served in this town – and it was always a privilege to work with him, and learn from him.

"I was proud to call him a close personal friend and confidant. He never let politics stand in the way of doing what was right, and that’s why he had the absolute respect of Republicans and Democrats alike. Today, our thoughts and prayers are with all of Warren’s family and friends." 

—This story was updated at 4:44 p.m.