He doesn't challenge them he ignores them. He is the only president to have never vetoed a bill. He very publically signs the bills with lots of photo-ops and press. But then after all is said and done he writes a "signing-statement" saying how he interprets the bill and does what he wants.
He did screw up on one of the them though. Well, he didn't screw up, he got caught. The House and Senate passed different versions of the budget bill. Bush knowingly signed a bill that he knew did not pass the House. Again - Bush signed and put into law a bill that did not pass the House of Representatives. Congressman John Conyer (D- Michigan) is suing him.
. . .
So, I am going to court. With many of my Democratic Colleagues (list appended at the bottom of this diary), I plan to file suit tomorrow in federal district court in Detroit against the President, members of the Cabinet and other federal officers seeking to have a simple truth confirmed: a bill not passed by the House and Senate is not a law, even if the President signs it. As such, the Budget bill cannot be treated as the law of the land.
. . .
Democrats file lawsuit over deficit-reduction law
4/28/2006, 12:21 p.m. ET The Associated Press
DETROIT (AP) — Eleven U.S. House Democrats filed a federal lawsuit Friday against President Bush and other administration officials, claiming that a $39 billion deficit-reducing law is unconstitutional because the president signed a version that differed slightly from the one the House passed.
The lawsuit, led by Rep. John Conyers, D-Mich., the ranking member of the House Judiciary Committee, was filed in U.S. District Court in Detroit. At least two other lawsuits about the legislation have been filed, one by an Alabama attorney and another by a Florida-based student loan consulting firm.
A version of the bill that was narrowly approved by the House on Feb. 1 contained a clerical error, which, according to the lawsuit, amounted to an additional $2 billion in spending. (link)
Bush challenges hundreds of laws
President cites powers of his office
WASHINGTON -- President Bush has quietly claimed the authority to disobey more than 750 laws enacted since he took office, asserting that he has the power to set aside any statute passed by Congress when it conflicts with his interpretation of the Constitution.
. . .
In his signing statements, Bush has repeatedly asserted that the Constitution gives him the right to ignore numerous sections of the bills -- sometimes including provisions that were the subject of negotiations with Congress in order to get lawmakers to pass the bill. He has appended such statements to more than one of every 10 bills he has signed.
. . .(link Boston Globe)