The Senate GOP began to mount its public relations campaign after Republican representatives locked arms to oppose the Democratic package in the House. All Republicans in the House voted against the package Wednesday night, though it still passed easily.
The bill had House Democrats' support, but Obama is looking for at least some Republican backers in the Senate where the Democratic advantage is not nearly as wide.
Republicans, though skeptical, still want Democrats to add more tax relief and strip out what they see as wasteful spending items that won't create jobs.
"This is about spending money we don't have for things we don't need," said Sen. Tom Coburn, R-Okla.
"At the end of the day, the way you get genuine bipartisanship is with serious Republican proposals included in the measure, and that didn't happen in the House and I think it's highly unlikely in the Senate," Senate Minority Leader Mitch McConnell told FOX News on Thursday.
"If the Senate version looks like I think it's gonna look, there'll be overwhelming Republican opposition in the Senate, and I don't think there'll be any way to characterize it as a bipartisan success story," he said.
House Republicans put up an alternative measure Wednesday that they claimed would create twice the jobs at half the cost. House Minority Leader John Boehner touted that proposal in a statement Thursday and said Republicans "made good" on a pledge to "not simply be the party of opposition."
While Senate Republicans are not using that legislation as a verbatim blueprint, they are pushing for several similar provisions.
Like their House colleagues, Senate Republicans are calling to reduce the two bottom income tax rates from 15 to 10 percent, and from 10 to 5 percent.
They also want a $15,000 tax credit for first-time homebuyers and a 4-to-4.5 percent mortgage rate for creditworthy first-time buyers. South Carolina Sen. Jim DeMint is pushing a plan that would lower tax rates for individuals and small businesses and, he says, create 7.5 million jobs over four years.
GOP senators stressed the need for more housing help at a press conference Thursday. They said they want a stimulus package -- just one that works.
"We've got to go slow, and we cannot accept this current package as it's written," Kentucky Sen. Jim Bunning said.
"This spending bill is too big, and it's going in the wrong places for the immediate stimulus that we're all looking for. ...Let's go to the heart of the problem: the housing industry and the credit markets," Texas Sen. Kay Bailey Hutchison said.
Arizona Sen. Jon Kyl said if Obama wants more GOP support, he'll need to have "key Republican concepts embedded in the legislation."
Alabama Sen. Jeff Sessions, though, said, "There's a growing and grim recognition, I believe, within our conference that there's very little likelihood of a significant change in this colossal spending bill."
Republicans are accusing Democrats in the Senate of upping the ante to nearly $900 billion and adding more special interest pork.
Among the provisions in the proposal are $400 million to prevent sexually transmitted diseases, $50 million more than the House approved; $25 million to rehabilitate off-roading trails for ATV's; $70 million for climate research; and $150 million for honey bee insurance.
The House plan largely reflects Obama's desires, but after zero GOP support, he suggested the House plan was hardly perfect.
"I hope that we can continue to strengthen this plan before it gets to my desk," Obama said.
The 244-188 House vote registered 177 Republicans unanimous in opposition.
Obama personally pledged to House and Senate Republicans in closed-door meetings on Tuesday that he is ready to accept modifications as the legislation advances.
Democrats had already dropped provisions that Republicans had mocked, including money to resod the National Mall and expand family planning programs.
The Senate bill contains a plan that would cost approximately $70 billion to make sure that about 24 million mostly middle-class taxpayers don't get hit by the alternative minimum tax. Although welcome by many lawmakers, the move wouldn't do much to boost the economy since the AMT "patch" is expected anyway later in the year if it doesn't pass now.
The Hill's A.B. Stoddard said Wednesday that an "entirely different bill" will likely come out of the Senate and that House Republicans will have a chance to vote for something more amenable. She said it will not include the tax relief Republicans are calling for but could include more stimulative spending measures.
Sen. Kent Conrad, the Democratic chairman of the Senate budget committee, signaled that the House version will be changed on many fronts.
"I think there's general agreement there has to be a substantial economic recovery package, but what came over from the House can be substantially improved," he said.
FOX News' Carl Cameron and Jim Angle and The Associated Press contributed to this report.