Updated: July 4, 11:54 a.m.

While White House officials have set their sights on beginning to withdraw troops from Afghanistan next summer, Sen. Joe Lieberman said Sunday that setting a timeline for winding down the war effort in that country would be a mistake.

The Connecticut Independent said setting a date to leave the country sends the wrong message to both the Afghan people and Taliban forces about the United States’ commitment in that region. “If conditions don’t allow it next July, I don’t think it’s going to happen,” Lieberman said in an interview on “Fox News Sunday.”

Lieberman’s comments about the July 2011 timetable for withdrawal were echoed by Sen. John McCain (R-Ariz.) on ABC’s “This Week” and Sen. Lindsey Graham (R-S.C.) on CBS’ “Face the Nation.” A timeline “sounds an uncertain trumpet,” McCain said. “Our commitment must be we will succeed, and then we will withdraw.”

The three Senators are spending the Fourth of July in Afghanistan, reviewing conditions on the ground and talking military policy with Gen. David Petraeus, who is in his first week as commander of U.S. and NATO forces in that country.

“What I want to hear from the White House and from the administration is, come July 2011, we can evaluate our progress,” Graham said. “And if you can transition, we will do so in certain areas, but everything will be conditions-based. If we don’t say that and mean it, people are going to hedge their bets, and we’re not going to be successful.”

Graham said Vice President Joe Biden, who is in Iraq for July Fourth, reassured him that a withdrawal would be based on conditions on the ground. “I take him at his word,” Graham said.

Lieberman and McCain were asked about the possibility of sending even more troops to Afghanistan to help turn the tide in a war that many on Capitol Hill believe is going against the United States.

McCain said it is a decision to be made later this year after a formal review is completed by U.S. officials, but Lieberman said he has encouraged Petraeus not to hesitate to ask for those troops if he believes he needs them.

On CNN’s “State of the Union,” a trio of House Members who are veterans of Mideast conflicts discussed the challenges Petraeus faces in his new role.

“This one-year deadline is weighing down on every commander’s shoulders. From the lieutenants to three-star generals, it’s weighing on everybody,” said Rep. Duncan Hunter (R-Calif.), who served two combat tours in Iraq and one in Afghanistan. “I think it’s going to be tough. I don’t think we can do it in a year.”

But Hunter, Rep. Mike Coffman (R-Colo.) and Rep. John Boccieri (D-Ohio) all agreed that nation building is beyond the scope of the U.S. military.

“We aren’t trying to make Iraq into San Diego. It’s never going to be San Diego. It’s always going to be kind of the Wild West. That’s how they are. Afghanistan is the same way,” Hunter said. “We’re never going to make it like we are here. They don’t want to be like we are here in this nation. So let them do what they do naturally, make sure they’re not a threat to us and that’s it.”

Boccieri said success will be gauged in Afghanistan by how well the new government can provide security for its people, especially in the remote provinces where the Taliban have previously thrived.

“You know, quite frankly, when the Taliban rolls in, those folks in those outlying areas are for the Taliban. When the Americans roll in, they’re for the Americans,” he said. “Until we have a strong, stable central government that can execute justice … it’s going to be a challenge.”

Lieberman also confirmed that one of Petraeus’ first tasks since taking charge has been to review the rules of engagement for troops under his command. He is trying to give his troops more clarity about how and when they can engage with the enemy.

“We’ve got to be concerned about the safety of our American troops here,” the Senator said. “I hope he clarifies them as quickly as possible.”