(CNN) -- The Senate on Tuesday continued wrangling over amendments to the $885 billion economic stimulus plan.
President Obama is hoping to get bipartisan support in Congress on the stimulus plan.
Ten Republican senators met in Florida GOP Sen. Mel Martinez's office Tuesday morning to discuss a stimulus measure that is broader than their leadership is proposing, but narrower than the Democrats' plan.
CNN was the only news organization outside the meeting.
Afterward, Martinez told CNN the details are still being debated and finalized, but they are looking at a ballpark figure of $500 billion, including the cost of tax cuts, infrastructure and military spending, and provisions to address the housing crisis.
President Obama wants a bill signed by Presidents Day -- 13 days from now. But before that can happen, the Senate must vote on its version of the bill, and then the House and Senate bills must be conferenced together.
The House passed its version of the stimulus plan last week without a single Republican vote. Republicans in the House and Senate want a plan with less spending and more tax cuts.
Martinez and Sen. Lindsey Graham, R-South Carolina, said they planned to present their ideas to fellow Republicans at their weekly policy lunch.
The eclectic group of Republicans, spanning the ideological spectrum from the most conservative to the most moderate GOP senators, assembled over concerns their leadership's approach -- to focus exclusively on the housing crisis and tax cuts -- is enough to jumpstart the economy.
Sen. Susan Collins, R-Maine, told CNN the group believes a "realistic alternative" to the Democratic proposal is needed. "The worst thing we can do is just say no," she said.
Sen. John McCain, R-Arizona, said they are trying to come up with a better package to create jobs.
The group of senators included McCain, Martinez, Saxby Chambliss of Georgia, Collins, Richard Burr of North Carolina, George Voinovich of Ohio, Tom Coburn of Oklahoma, John Thune of South Dakota, Johnny Isakson of Georgia and Graham.
The president has been pushing for bipartisan support on the package. He met Monday with Democratic congressional leaders in hopes of stripping out some of the controversial provisions and working toward common ground with Republicans. Watch more on Obama's bipartisan push »
Sources say that the Obama team is urging Senate Democrats by phone and behind closed doors to remove some of the spending critics say won't stimulate the economy and add job-producing public works projects like roads and bridges.
Even as the White House quietly pushes the Senate, it is calling in reinforcements via its massive e-mail list of supporters, which was collected during the campaign and has been turned into a lobbying/re-election tool.
The Democratic National Committee used the list to send an e-mail from the president urging supporters to attend weekend meetings to learn about the economic recovery plan.
Democrats on Monday dropped two controversial spending programs in attempt to placate Republicans: $75 million for anti-smoking programs and $400 million to prevent HIV and other sexually transmitted diseases.
Two Democratic leadership sources told CNN they did it as a "symbolic gesture" to show Republicans they are listening to their objections. Watch: What does Obama need to do to get the plan passed? »
But one of the Democratic sources also admitted that "it's hard to explain when you're in the midst of a crisis why these programs are important. When people are struggling and thinking about their jobs, it's hard to make that connection."
Republicans, and some Democrats, have been pointing to both of these items as prime examples of "excess spending" that doesn't belong in this stimulus bill.
But there are many other programs Republican senators and some conservative Democrats still want to scrub from the bill.
A group of Republican senators has drafted an alternative stimulus measure that narrows government spending to bolstering infrastructure and helping unemployed Americans, addresses the housing crisis and relies mostly on tax cuts.
The $713 billion plan was put together by Florida Sen. Mel Martinez, who has been working with a handful of other GOP senators. It includes $430 billion in tax cuts; $114 billion for infrastructure projects; $138 billion for extending unemployment insurance, food stamps and other provisions to help those in need; and $31 billion to address the housing crisis.
The draft Martinez put together is a broader approach than what some GOP leaders have suggested. Senate Minority Leader Mitch McConnell, R-Kentucky, and other Republicans appear to want to limit the stimulus to cutting taxes and addressing the housing crisis.
But Martinez's draft is narrower than the Democrats' plan because it eliminates spending on government programs that Republicans and some Democrats say shouldn't be in the bill because they don't create jobs.
Martinez has just started showing the plan to his colleagues, and it is too early to tell how much traction this idea will get among other lawmakers.
McConnell on Monday dismissed the idea that Republicans are trying to block passage of the economic stimulus plan. "Nobody that I know of is trying to keep a package from passing," he said at a news conference. "We're trying to reform it."
GOP leaders in the House on Monday put out a list of what they call wasteful provisions in the Senate version of the stimulus bill. Some of the measures include:
• $650 million for the digital television (DTV) converter box coupon program.
• A $246 million tax break for Hollywood movie producers to buy motion picture film.
• $1 billion for the 2010 census.
• $248 million for furniture at the new Homeland Security headquarters. Read the list of 'wasteful' items
The $819 billion bill that passed in the House last week is two-thirds spending and one-third tax cuts.
Much of the $550 billion in spending is divided among these areas: $142 billion for education, $111 billion for health care, $90 billion for infrastructure, $72 billion for aid and benefits, $54 billion for energy, $16 billion for science and technology and $13 billion for housing.
One change already made in the Senate version is the addition of $71 billion to fix the Alternative Minimum Tax, which was intended to place a tax on the wealthy but now hits many middle-class families.
The Senate bill also adds a $300 payment to seniors, disabled people and others who can't work, and suspends taxes on the first $2,400 of unemployment benefits.
CNN's Dana Bash and Candy Crowley contributed to this report.