Lawmakers are still hammering out a compromise on the Bush tax rate extension, but the White House Tuesday pressed for Republicans to help pass another controversial piece of legislation - the DREAM Act.

"We're expecting a vote in the Senate quite likely to be tomorrow," White House Director of Intergovernmental Affairs Cecilia Muñoz said in a conference call with reporters, though by some other estimates the bill won't hit the Senate floor until later in the week. "There is a tremendous amount of work going on both in the building where I work, but also around the country to make sure this is a positive vote."

The conference call, which stressed the immigration legislation's potential positive impact on military readiness, was the third call from administration officials advocating for the DREAM Act in less than a week.

The legislation would create a path to citizenship for young illegal immigrants who were brought to the United States by their families, provided they attend two years of college or join the armed forces; an option Under Secretary of Defense for Personnel and Readiness Dr. Clifford Stanley said will help the military maintain recruitment and attract educated personnel.

"There are a lot of things going on right now, that we need smart people who can think," Stanley said, adding that where recruits were born is inconsequential. "This is not an American versus illegal alien issue...we're looking at the highest standards, period."

Muñoz highlighted past bipartisan support for the legislation. "It looks very much like the outcome is going to depend on whether or not we have similar or near that level of Republican support," she said.

But many conservatives have said the DREAM Act shouldn't be on the lame duck docket, and some have voiced concern that even Sen. Majority Whip Dick Durbin's (D-IL) current watered-down draft of the act just rewards those who enter the country illegally. Political prognosticators predict that the latest version, which nixes a provision allowing illegal immigrants to pay in-state college tuition rates and bars recipients from benefiting from health care exchanges, is unlikely to draw the 60 votes needed for passage in the Senate.

"Comprehensive immigration reform should be thoroughly debated in a[n] open amendment process prior to a vote on the DREAM Act, which in its current draft raises several serious concerns for me," Nevada Sen. John Ensign (R) said in a statement Monday. "This lame duck session will not provide the time necessary to debate this issue thoroughly."

In a Sunday interview with Fox News, Sen. Jeff Sessions (R-AL) equated the proposal to "unrestricted amnesty," arguing that the bill is "filled with loopholes" and that it would show illegal immigrants that the U.S. has "given up on enforcement of our immigration laws."

"We disagree wholeheartedly with Senator Sessions' assessment that this is an amnesty," Muñoz said. "What this does is give people...an opportunity to receive protection under the law, but in exchange for a deep commitment on their part," she explained, arguing that the requirement to pursue education or join the military is "very, very far from an amnesty."

"We believe again, if the Congress is moving past politics and looking at what's good for the country, that we will see a strong vote tomorrow," Muñoz concluded.