Harry Reid, the senate Democrat leader who accused Bush of having "put our troops in the middle of a civil war", said: "The president is inviting us down to the White House with preconditions. That's not the way things should operate."
Bush has refused to negotiate on Democrat demands for a date for a US withdrawal from Iraq.
"We can discuss the way forward on a bill that is a clean bill; a bill that funds our troops without artificial timetables for withdrawal, and without handcuffing our generals on the ground," Bush said during a speech to the American Legion veterans group in Washington.
Bush threatens veto
Last month, the House of Representatives and the senate passed bills with more money for the war than Bush had requested.
"We're going to give the president a bill. And it is up to him whether he wants to fund the troops"
Harry Reid, senate Democrat leader
But in approving the money, Democrats attached deadlines for the US role in Iraq: a deadline of September 1, 2008, in the House bill and a goal of March 31, 2008 in the senate legislation.
Reid told reporters he and fellow Democrats were now pushing ahead with a bill that would strike a compromise between the House and the senate legislation.
"We're going to give the president a bill. And it is up to him whether he wants to fund the troops," he said.
Bush has threatened to veto the bills, saying Democrat leaders in congress will be to blame for any delays in funding to US troops, because they are proposing legislation that he will refuse to sign.
"We are at war. It is irresponsible for the Democratic leadership in congress to delay for months on end while our troops in combat are waiting for the funds they need to succeed," Bush said.
Samir Shakir Sumaida'ie, Iraq's ambassador to the US, also criticised the Democrats' proposed timetables for withdrawing American troops from Iraq. "For Americans to abandon this effort halfway would be fatal," he said.
To signal the intention to withdraw by a certain date would be seen as the beginning of the end, and would be hailed as a victory by our enemies who will no doubt press their advantage," Sumaida'ie wrote in the Wall Street Journal on Tuesday.