Worried Congress' support for Iraq is deteriorating rapidly, Baghdad dispatched senior officials to Capitol Hill this week to warn members one-on-one that pulling out U.S. troops would have disastrous consequences.

The lobbying push targeted Republicans and Democrats alike, but focused primarily on those considered influential on the war debate. On Thursday, hours before the House voted to limit funds for the war, Iraqi Deputy Prime Minister Barham Saleh met with more than 30 House Republicans and more than a half-dozen senators, including Sens. Harry Reid, D-Nev., John Warner, R-Va., and Hillary Rodham Clinton, D-N.Y.

"He understands that American patience is waning," said Sen. Norm Coleman, after eating lunch with Saleh, Iraqi Ambassador Samir Shakir al-Sumaidaie and Sen. Saxby Chambliss.

But the lobbying by the Iraqis isn't the only pressure-point being applied in Washington.

Clinton said Friday she considered it "promising" that several Republican House members went to the White House and told President Bush they believe the continuing war is adversely affecting the party.

She said the GOP lawmakers told Bush pointblank that "he has to change course in Iraq." But she also said she didn't think that Bush was ready to reverse course.

"I think we're going to go back and forth on this for a while longer," Clinton said in an interview Friday on MSNBC's "Morning Joe" program with Joe Scarborough.

"It is clear that whatever the mission used to be, it is either accomplished or over," she said. "If there are remaining American interests, then let's spell them out."

Baghdad's ability to sell members like Coleman, R-Minn., and Chambliss, R-Ga., on the war effort is critical if the Iraqi government wants U.S. troops to stay. Coleman in recent months has become deeply skeptical of the president's decision to send additional troops to Iraq and says patience on the war in general is limited.

Coleman, Chambliss and Sen. John Sununu, R-N.H., who met separately with Saleh, will be up for re-election next year — facing voters who have grown tired of a war in its fifth year and that has killed more than 3,380 troops. While Republicans have been reluctant to intervene, many say President Bush has until September to tell if the troop buildup in Iraq is working before they demand another approach.

With the clock ticking, Saleh — a Kurdish politician highly regarded by U.S. officials and who speaks impeccable English — said he came to Capitol Hill to convey the "imperative of success" in Iraq.

"Iraq is a central battleground in this historic conflict" against terrorism, he said in a brief interview after meeting with Reid, the Senate majority leader.

His trip came on the heels of a visit by Mowaffak al-Rubaie, the national security adviser to Iraqi Prime Minister Nouri al-Maliki, along with three other senior advisers, according to the Iraqi embassy. The New York Times first reported al-Rubaie's visit on Tuesday.

The timing of these meetings is no mistake. This month, Congress is expected to send Bush legislation that funds the war in Iraq but requires the Baghdad government meet certain political and security reforms. In question is what consequences the Iraqis should face if they fail. Democrats want U.S. troops to leave, Republicans say they don't want to force redeployments, but some say they would be open to withholding more than $5 billion in foreign aid.

The House voted 221-205 Thursday for a stronger measure that would fund the war only through July, giving Congress the option of cutting off money after that. The bill is unlikely to survive in the Senate, although it indicates the war's unpopularity among members and their frustration with the lack of progress in the Iraqi parliament.

The most recent irritant among U.S. lawmakers was a report that Iraqi officials would break for two months this summer.

"Our armed forces are up to 150,000 troops; we're over $600 billion appropriated for this, lost 3,300 lives, 25,000 wounded fellow citizens. ... And the Iraqi answer? We're taking a summer off. Goin' fishing," said Rep. Rahm Emanuel, D-Ill.

Saleh said he expects the vacation to be shortened by at least a month, although nothing had been decided. He added that Iraqis value being independent and do "not take kindly of (U.S. officials) telling us when to recess."

Democrats seemed to consider these meetings with Iraqi officials as beneficial — if only to convey their frustration to Iraqi officials in person.

Reid's spokesman Jim Manley said the senator told Saleh that "U.S. patience, blood and treasure were not unlimited and that the Congress would be taking a more decisive role in the coming weeks and months."

"Salih understood the point, and said he would deliver the message to the Iraqi cabinet," Manley added.