A weekly roundup of the buzz from the Sunday talk shows

The White House and Republican allies were optimistic that the immigration overhaul bill will come back to life and pass the Senate, as they hinted they will pitch the bill as necessary to securing the border and enforcing the law, appealing to conservatives wary that illegal immigrants will continue to stream into the country.

"It is the largest investment ever in border security," White House press secretary Tony Snow said on "Fox News Sunday." "We have a mechanism now for knowing who the illegals are, where they are, whether they're working, whether they're breaking the law."

Commerce Secretary Carlos M. Gutierrez said the White House will emphasize that the immigration proposal "is first and foremost a national security bill." People might say, "Just go ahead and enforce the law," said Gutierrez, speaking on CNN's "Late Edition." But, he added, "our laws are insufficient." The keys in the bill include requiring workers to carry a tamper-proof, biometric identification card and mandating that employers use a worker eligibility-verification system, he said.

Sen. Richard J. Durbin (Ill.), the Democratic whip, suggested that Democrats will allow debate to resume if Republicans promise to limit the number of amendments they try to debate.

MCCAIN'S TIMELINE: Sen. John McCain (R-Ariz.), who said he is going to support the U.S. troop increase in Iraq even "if I'm the last man standing," acknowledged that time is running out for substantial signs of progress there.

"I read the polls and I know what American public opinion is, and I regret that now September seems to be a magic moment," McCain said on ABC's "This Week." He said the government of Prime Minister Nouri al-Maliki has to show "fairly soon" that it can govern effectively.

By Zachary A. Goldfarb