Democrats won control of the Congress largely on an anti-Iraq War message. The newly elected members promised to end the War. Everyone expected that President Bush would have to adjust to the new reality.
He announced a surge of troops and more spending in Iraq. Democrats who had vowed to not fund more military activities in the region, especially if not paid for, soon caved in and supported the troops.
The President used all of his powers to pursue what he though was right, irregardless of what all the political class thought the election was about.
Doing the right thing in this case would be popular with Democrats and eventually with Democratic leaning independents.
The President and Ms. Pelosi should develop a strong agenda and fight for it.
You can't have as you plan: compromise.
A real compromise is only possible after you've demonstrated you can win on your own.