In fact, Sen. Arlen Specter (R-PA) is promising to have a bill ready soon after senators return from a two-week recess.

Specter told “Fox News Sunday” that he thinks tempers will cool over the two-week hiatus, and that senators will get feedback from constituents about the failure to pass a bill.

A compromise measure appeared ready for passage on April 7, but fell victim to internal disputes and political maneuvering. Top Republicans blamed the Senate’s Democratic leader, Harry Reid.

The bill would have required stronger border security, regulated the future entry of foreign workers, and created regulations for illegal immigrants already in the country.

The House earlier passed a tougher, more controversial bill that contains the dreaded HR 4437 that will criminalize undocumented aliens.

Meanwhile, throngs of immigrants, both legal and illegal, held a massive waive of demonstrations that took place Monday in dozens of cities nationwide, including New York City, Jersey City and Philadelphia.

In Manhattan, flag-waving demonstrators filled the streets around City Hall in Lower Manhattan, vowing to keep pressing Congress to give undocumented immigrants a path to legal residency in the United States.

The Hispanic-dominated crowd, estimated by the organizers at 125,000, stretched from City Hall into the side streets and up Broadway as far as Grand Street. Speakers rallied the crowd from a stage and three giant video screens, but marchers blocks away could hear only the thundering chants around them.

Dozens of Filipinos joined the 3 p.m. rally led by the Justice For Immigrants (J4I) Filipino Coalition, and is part of an effort called a National Day of Action for Immigrant Justice.

The Filipino contingent met an hour before the mass action at the northeast corner of Broadway and Wall Street. They were holding placards and banners urging for “legalization and full rights for immigrants, not criminalization.”

In Jersey City, over 3,000 rallied at Liberty State Park, with the Statue of Liberty and Ellis Island — two most potent symbols of American immigration — in the backdrop.

“If you’re a Filipino in the United States, it’s time to wake up,” says Berna Ellorin of J4I, calling for solidarity among Filipinos, legal and illegal.

The coalition said Filipinos are the third largest immigrant group (next to Mexicans and Chinese) and the second largest Asian community in the United States.

An estimated 1 million Filipinos are in the country illegally, it says.

In Washington, D.C., Filipino-American Sasha Angara Bennet wore a white T-Shirt with colors of a Filipino flag as she joined the crowd chanting, “Justice, Justice!”

Bennet, born in Nigeria to an American father and Filipino mother who have since divorced, obtained her U.S. citizenship when she reached 21. She then sponsored and won permanent residency for her mother, “who overstayed her tourist visa.”

Holding a flag with the words “Proud to be a Filipino-American,” she told Agence France Press:

“Like me, many children of illegal immigrants born in the U.S. are waiting to be 21 years so that they can also sponsor their parents for permanent residency. We should not deprive them of citizenship.”

Under the Senate compromise, undocumented aliens who are in the U.S. for over five years could work for six years and apply for permanent residency without having to leave the U.S., on condition that they paid fines and taxes, learned English and passed other tests.

Those who are here from two to five years would have to go to border entry points sometime in next three years, but could immediately return as temporary workers. Those here less than two years would have to leave and wait in line for visas to return.

Any measure passed by the Senate would have to be merged with a bill passed by the House. The House bill, sponsored by Rep. James Sensenbrenner (R-WI), contains no path for legalization.

Rather, it calls for the construction of a 700-mile fence along the U.S.-Mexico border and the categorization of undocumented immigrants as felons, without offering them any lawful employment.

Security was tight at the Jersey City rally in anticipation of counter demonstrations from anti-immigrant groups.

The only sign of such opposition came in the form of an airplane circling overhead, with a banner addressing the crowd below with a racial epithet for Mexicans — the biggest group of illegal immigrants in the U.S.

“No Amnesty — beaners go home,” the banner read.

A Washington Post-ABC News poll released on Monday showed that 75 percent of Americans believed U.S. authorities were not doing enough to stop illegal immigration, but 63 percent favored a program that would lead to legal status and permanent citizenship for illegal immigrants.

President George W. Bush has been urging Congress to approve a temporary worker program that would allow illegal immigrants to remain in the country and have some legal status.

Speaking after a speech on the war on terror in Washington on Monday, Mr. Bush said the demonstrations were “a sign that this is an important issue that people feel strongly about.”

But House members remained adamant on the issue.

“You have to remember, illegal aliens are just that, illegal,” House Majority Leader John Boehner said on ABC’s “This Week” program on Sunday.

Rep. Tom Tancredo (R-CO), chairman of House Immigration Reform Caucus and one of the leading opponents of legislation that would allow illegal immigrants to remain in the country and work toward citizenship, called the stalemate on the Senate bill last week “a good day for America.”