Washington (CNN) -- A federal budget compromise that already passed the House cleared a key procedural hurdle on Tuesday in the Senate, increasing the likelihood it will win final Congressional approval this week.
President Barack Obama has signaled his support for the plan worked out by the budget committee leaders in each chamber that would guide government spending into 2015 to defuse the chances of another shutdown such as the one that took place in October.
Tuesday's vote overcame a Republican filibuster attempt that required 60 votes in the 100-member chamber to proceed on the budget measure. The count was 67-33, with a dozen Republicans joining the 55 Democrats and independents in support of the plan.
Final approval in the Senate requires a simple majority of 51 votes. The budget plan easily passed the House last week on a 332-94 vote.
The politics of the issue were clear in Tuesday's vote breakdown. Only one Republican Senator facing a primary challenge in their re-election campaigns voted with Democrats to overcome the GOP filibuster -- Lamar Alexander of Tennessee.
Alexander has indicated he will oppose the budget plan in the final vote later this week.
A new ABC News/Washington Post poll released Tuesday showed 50% of respondents approving of the budget plan while 35% opposed it. According to the survey, a majority of Democrats and independents backed the proposal, while only 39% of Republicans liked it.
Some Senate Republicans said before Tuesday's vote that the most important thing for now was to lower the budget deficit, even if only by a small percentage, and prevent further government shutdowns like the 16-day stoppage in October that proved politically damaging to the GOP.
Sen. Ron Johnson, who was lobbied to support the bill negotiated by fellow Wisconsin Republican Rep. Paul Ryan, said he wanted "to make sure we avoid any additional government shutdowns."
"The federal government does enough harm to our economy," Johnson said. "We don't need to add additional harm by this crisis management. In the end this is not the kind of deal I would want to see. I'm sure it's not the kind of deal Paul Ryan would want to produce."
Conservative GOP Sen. Orrin Hatch of Utah said in a statement that "sometimes the answer has to be yes."
"Ultimately, his agreement upholds the principles conservatives stand for and, with Democrats controlling the White House and the Senate, it is the best we can hope for," he said of the plan Ryan negotiated with Democratic Sen. Patty Murray of Washington.
Final congressional approval of the elusive budget agreement would mark a rare win for bipartisanship and a step up for a Congress infected with political dysfunction and held in low public esteem with midterm elections less than a year off.
Democrats wary, too
While Democrats supported the bill, many had concerns.
More liberal senators -- like Tom Harkin of Iowa -- complained that an unemployment benefit extension was not included in the deal.
"There's over a million people now who cannot find a job, out of work, and right at this time of year their unemployment insurance is being cut off," Harkin told Radio Iowa last week. "It's really unconscionable."
The budget agreement, which was months in the making, eases spending caps for the next two fiscal years while softening the impact of across-the-board spending cuts, known as the sequester, on defense and non-defense programs.
Overall, it calls for more than $20 billion in deficit reduction.
Current federal spending expires in mid-January, raising the possibility of another shutdown at that time if there's not a new agreement in place to keep federal coffers filled.
The strong vote in the House on the budget plan on Thursday brought a collective sigh of relief among supporters, who initially thought it would sail through the Senate, where bipartisanship has been more the norm than in the sharply divided House.
But after reading details of the agreement, many Senate Republicans -- including several in leadership positions -- came out against the bill.
"I'd really like to stay within the (spending) caps," complained GOP Sen. John Boozman of Arkansas. "This busts the caps and as a result I'll vote against it."
Republican Sen. Lindsey Graham of South Carolina complained that the plan reduces military benefits.
2016 in play
Three leading tea party-backed senators with 2016 presidential aspirations -- Rand Paul of Kentucky, Ted Cruz of Texas, and Marco Rubio of Florida -- also have come out against the budget compromise for similar reasons.
CNN's Dana Bash, Paul Steinhauser and Dan Merica contributed to this story.