Mr. Frank, anticipating a veto pledge, said on Tuesday evening that a veto would signal that the president was abandoning efforts to help homeowners and would mean that “he’s stopped trying to govern.” Moreover, Mr. Frank and other Democrats said Republicans in the Senate would read the president’s remarks as a signal that they should stand fast against the Frank-backed bill if it reaches their chamber.

Though Democrats enjoy a considerable advantage over Republicans in the House (235 to 199, with 1 vacancy), and some Republicans have been gravitating toward the Frank bill, the political math would appear to be in the president’s favor. Even if Mr. Frank’s bill sailed through the House with the two-thirds majority needed to override a veto, the odds of the Senate passing it with the necessary two-thirds majority would be much slimmer, since the Democrats control the Senate by only 51 to 49.

With six months to go until his successor is chosen, Mr. Bush is sometimes referred to as a lame duck. But as he spoke on Wednesday on the north portico of the house he will soon vacate, he showed his unwillingness to surrender power before he has to.

He called on Congress to pass a $108 billion war-supplemental bill “without any strings,” meaning anything that smacks of a withdrawal timetable for Iraq; to give his Colombia free-trade agreement “an up-or-down vote” instead of letting it stall in the House; to make his “temporary” tax cuts permanent, and to allow “environmentally friendly domestic exploration” for oil.

The reference to oil exploration sounded like an allusion to the Arctic National Wildlife Refuge, which the president has long said can be explored in a way that would do no damage while enhancing energy independence. The House has endorsed the idea a dozen or more times in recent years, but it has always stalled in the Senate.