U.S. Senate Majority Leader Harry Reid plans to forge ahead with a vote on the DREAM Act, said his spokesman, Jim Manley.
"We intend to have a vote," Manley said. "We're still trying to figure out when."
Republicans have threatened a filibuster on the DREAM Act, which would grant certain undocumented youth conditional legal status and a chance to pursue U.S. citizenship. Democrats, led by Reid, a Nevada Democrat, have tried to buy time to secure more votes and, they hope, a better chance for passage.
But the DREAM Act, which passed the House of Representatives last week, is not standing on strong ground at the moment, say people on both sides of the debate.
The bulk of the attention this week in Congress so far has been on the tax-cut package negotiated by President Obama and Congressional Republicans. Republicans have said they will not give serious consideration to other matters until congressional action on the tax-cut package is completed.
"They said they're not going to vote on anything unless there's a tax vote," said Sen. Robert Menendez, long one of the Senate's most vocal proponents of giving certain undocumented immigrants a pathway to legalization. "The Republicans have been voting against everything in lockstep."
"In view of the fact that House passed the DREAM Act, they could have voted on that [House version]," Menendez, a New Jersey Democrat, said. "But the cloture vote got voted down."
A cloture vote ends debate on a bill, setting the stage for a vote.
Most Republicans in Congress strongly oppose the DREAM Act, and vow to work against its passage.
Rep. Steve King, R-Iowa, who favors strict immigration enforcement, said he feels certain the Senate will not approve a DREAM Act measure.
He said Democrats were wrong to try to push through the bill during the lame-duck session.
"There's no time to evaluate it, no opportunity to amend it," King said.
Many of the legislators dealing with matters in the lame-duck session, King said, "have been invalidated" by defeats in the November elections.
"Unless the Republicans join us, we can't win," Menendez said.
The DREAM Act, which stands for the Development Relief and Education for Alien Minors, calls for providing a road to legislation for children who are under 16, have lived in the country for at least five years, and commit to two years of college or the military. Students could also attend college at in-state tuition rates, which tend to be far less expensive than out-of-state costs.
Immigration advocates vow to fight to the finish.
Tonight, advocates around the nation plan to have a "telephonic town hall" to help keep up momentum for the DREAM Act, said Katherine Vargas, press secretary for the National Immigration Forum in Washington D.C.
"We're expecting a vote in the Senate this week, given the victory in the House last week," Vargas said. "If they have a vote on cloture on Thursday, then they could be ready to vote next week."
Faith leaders from various states were in Washington D.C. today, visiting congressional offices and trying to drum up support for a Senate passage of the DREAM Act.
"Activists will continue to push," Vargas said.
The bill is seen by advocates for undocumented immigrants as the best hope for legislation that would help legalize some of the nation's estimated 11 million illegal residents.Repeated efforts over the years to pass a comprehensive immigration reform measure failed.
Political leaders and immigrants rights groups who wanted a path to legalization for undocumented immigrants who met a strict set of criteria then narrowed their focus, putting their energy behind the DREAM Act.
They believed the DREAM Act had a better chance of getting the support of the American public because it pivoted on the notion of innocent children penalized because of the actions of their parents.
Democrats were intent on trying to pass the legislation through the lame-duck session, just before Republicans take control of the House of Representatives next month.
Republicans and activists who oppose giving any kind of break to undocumented immigrants fiercely opposed the measure, dismissing it as a form of amnesty for law-breakers. American residents, they have argued, should not have to foot the bill or give up slots in college classrooms so that young immigrants without documents could prosper.
Elizabeth Llorente is Senior Reporter for FoxNews.com, and can be reached at Elizabeth.Llorente@Foxnews.com. Follow her on Twitter @Liz_Llorente.