WASHINGTON — President Obama’s jobs bill meets its first big test on Tuesday as the Senate moves toward a vote on whether to take up the legislation, the centerpiece of Mr. Obama’s efforts to revive the economy.

If that effort fails to achieve the necessary 60 votes, as many Republicans and some Democrats predict, Senate Democrats may try to break up the bill into more palatable pieces and press for votes on the individual parts.

That is what Mr. Obama said was his preference in what almost sounded like an outright acknowledgement that Congress would reject his jobs proposal. “If they don’t pass the whole package, we’re going to break it up into different parts,” Mr. Obama said Tuesday during a jobs-related meeting in Pittsburgh, echoing White House officials who have said that they would seek to push those parts of the bill with the most chance of passage.

Alternatively, if the bill does not pass, Senate Democrats might join a handful of Republicans in searching for areas where the two parties might agree — a formidable challenge in a chamber where comity seems to worsen by the week.

In speeches around the country, Mr. Obama has assailed Republicans for blocking his jobs bill. While Mr. Obama can count on the support of a majority of Senate Democrats, a few moderate-to-conservative Democrats, including some who have to face re-election next year in states the president lost in 2008, have said they were leaning against the bill or refused to say how they would vote.

House Republican leaders have said they do not intend to take up the president’s $447 billion jobs bill as a whole, but might push favored pieces of it.

The House majority leader, Representative Eric Cantor, Republican of Virginia, welcomed reports that the president might support a piecemeal approach to jobs legislation, if the Senate declined to take up his full $447 billion package.

Mr. Cantor said he hoped “the president will drop his all-or-nothing approach and begin to work with us on areas of commonality” — initiatives that could promote hiring and economic growth.

“We are willing to take up the things we can agree on,” Mr. Cantor said. These, he said, include trade agreements, tax credits for the hiring of veterans, and measures to increase access to capital for small businesses - - but not tax increases or big domestic spending programs like the 2009 stimulus law.

The bill is a mix of public works spending and temporary tax cuts intended to respond to what Mr. Obama calls an economic emergency.

Burned by their experience over the summer during negotiations on the debt ceiling, White House officials have generally not negotiated with Republicans on the jobs bill, believing such talks would be futile in view of the huge gap between the parties on how to revive the economy.

Republicans said Mr. Obama was using the bill as a platform for his re-election campaign.

In an interview with ABC News last week, Mr. Obama said he did not think Americans were “better off than they were four years ago,” despite his efforts to improve the economy.

Fourteen million Americans are unemployed. The unemployment rate — 9.1 percent for the last three months — is higher than when Mr. Obama took office. And job-creation efforts have fallen short of White House hopes. The Labor Department says that nonfarm payroll employment totaled 131.3 million in September, compared with 132.8 million in February 2009, when Congress approved an economic stimulus bill championed by the president.

The jobs bill calls for $175 billion in new spending on highways and other public works, extension of unemployment benefits and aid to states to prevent teacher layoffs. The bill would also provide $272 billion worth of tax relief for individuals and businesses, including further cuts in payroll taxes and accelerated deductions for business investments.

Senate Democrats had revised Mr. Obama’s proposal so that the cost of the bill would be offset by a surtax of 5.6 percent, starting in 2013, on personal income in excess of $1 million. Fewer than 350,000 tax returns showed income of more than $1 million this year, according to the Congressional Joint Committee on Taxation.One of the more popular items in Mr. Obama’s jobs bill is a further cut in payroll taxes, intended to increase take-home pay for 160 million Americans. Congress last year reduced the Social Security payroll tax rate paid by employees to 4.2 percent, from 6.2 percent.

Under Mr. Obama’s proposal, workers would pay 3.1 percent next year — just half the normal rate, applied to the first $106,800 of wages. Republicans and some Democrats objected to tax proposals by the president that would have increased taxes for many couples making more than $250,000 a year. Democrats have rallied around the “millionaires’ tax,” a populist proposal that they say highlights their differences with Republicans.

“While the wealthiest prosper, the middle class stagnates,” the White House says in documents arguing for the jobs bill. Moreover, it said, citing statistics from the Internal Revenue Service, “1,470 millionaires and billionaires paid zero taxes in 2009.”