(CNN) -- President Obama's economic stimulus plan cleared its first hurdle, but it was hardly the bipartisan victory he hoped for -- not a single House Republican broke ranks to support it.

The stimulus bill now moves to the Senate, where GOP members want less spending and more tax cuts.

In fact, 11 Democrats also voted against the $819 billion package.

But a win is a win, and so the White House strategy is to take the long view: Maybe the Senate will take out more of the controversial pork projects and tweak the tax cuts to win over more Republicans.

The full Senate will vote on its version next week. Should the Senate and House pass different versions, the two bills would have to be conferenced together. Then both chambers would have to vote on the new conference version in the coming weeks. Watch what's next for the stimulus »

"I do think it is so important that we slow this bill down in order to do it right," said Sen. Kay Bailey Hutchison, R-Texas.

Senate GOP sources report that there is a "real split" in the GOP caucus about the best way to proceed in the wake of Wednesday's vote in the House.

The sources say Sen. Mitch McConnell, the Senate minority leader, wants a "smaller, narrower" bill. Another group of Republicans including Sen. John McCain of Arizona and Sen. Susan Collins of Maine is working to craft a larger package that would include more infrastructure spending.

Generally, the sources say, the party is looking for more concessions from the White House on spending.

The Senate has already made some changes in its version of the bill, which is approaching $900 billion.

The Senate Finance Committee added about $70 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 adds more direct money for seniors, with a plan to send $300 checks to social security recipients and disabled veterans. Smaller changes in the Senate version include $108 million to extend worker retraining programs and a provision to block any taxes on the first $2,400 of unemployment benefits.

Aides say housing relief is also going to be a big issue for some Republican senators. The main concerns are similar to those of their House counterparts. They want more tax cuts and less spending.

"We look forward to offering amendments to improve this critical legislation and move it back to the package President Obama originally proposed -- 40 percent tax relief, no wasteful spending and a bipartisan approach," McConnell said.

Obama has made it clear that he's not willing to budge on some of the big ticket items, like how the tax cuts are structured.

The version passed in the House 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.

Those opposed to the bill say it includes too much wasteful spending, pointing to things like $335 million in funding for education on sexually transmitted diseases and $650 million for digital TV coupons. Watch why some say there's too much pork »

A growing number of Republicans and Democrats say measures such as those don't create jobs.

The Democratic rationale is that healthier Americans will be more productive. And on the millions for digital television coupons, the hope is that money will go to new call centers explaining how the technology works.

"There's something in there for literally every interest. It's a pent-up wish list of spending programs that many around here have wanted to implement for a really long time," said Sen. John Thune, R-South Dakota.

Congressional leaders did drop some of the controversial provisions, like one that provided $200 million worth of contraceptives to low-income families.

Obama personally called some House Democratic leaders to urge them to remove the family planning provision in hopes of winning bipartisan support.

The White House is hoping that some Republicans will come on board in the Senate, where there already has been a little more compromise and a greater sense of bipartisanship.

Some House Republicans have left the door open to being more receptive to changes made on the Senate side, and then perhaps voting yes if they get those changes when the final bill comes up for a vote.

David Gergen, a senior political analyst for CNN, said that while there will be disagreements, some version will likely pass in the coming weeks.

"I think both sides are approaching this with some qualms, but they also feel -- especially the Democrats feel -- they have no choice. The economy is in urgent need to be addressed with a stimulus package," he said.

"We have got a very popular president. They're going to support him and go forward. And this package is going to pass. A version of this package is going to pass here in the next two or three weeks."

The president hopes to have the plan passed by Congress and on his desk for signing by mid-February.

CNN's Jim Acosta, Lisa Desjardins, Gloria Borger, Ed Henry, Kristi Keck and Brianna Keilar contributed to this report.

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