One poll, issued Wednesday by Gallup in Princeton, N.J., said 45 percent of those surveyed would rather the $85 billion in sequester cuts agreed to by Congress and the White House in 2011 not go into effect Friday as scheduled. Thirty-seven percent said they favor letting the cuts happen and 19 percent said they had no opinion.
The other poll, conducted by The Wall Street Journal and NBC News, revealed a narrower divide, with 50 percent against sequestration happening and 46 percent leaning the other way.
The cuts represent between 2 percent and 3 percent of the government's annual $3.5 trillion budget and big-ticket programs such as Social Security and Medicare benefits are exempt.
The Gallup poll found 60 percent of Americans said they were following the news about the budget cuts closely.
Gallup also said President Obama and congressional Democrats and Republicans all fall short of majority approval for their handling of the sequestration issue, with the president at 45 percent, Democrats at 37 percent and Republicans at 25 percent.
In the WSJ/NBC poll, 46 percent agreed allowing the spending cuts to take effect may not be perfect, but the country needs to take dramatic action to cut the burgeoning federal deficit, now at $16.6 trillion and growing about $1 trillion a year.
If they could swap in a new plan, a slight plurality of 39 percent said they'd prefer even deeper cuts, while a similar plurality of 37 percent said they'd want a plan with fewer cuts.
At the same time, 51 percent of those polled said the budget negotiations between Obama and congressional Republicans made them feel less confident the economy was getting better, while 16 percent said it made them feel more confident.
Both of these figures are the same as when this question was first asked in last month's WSJ/NBC poll.
About 29 percent said they thought the budget negotiations made no difference to the economy and 4 percent said they weren't sure. Last month, 31 percent said they thought the talks made no difference and 2 percent said they weren't sure.
Nearly six in 10 -- 59 percent -- said they thought the country was on the wrong track, the highest number since last summer. About one-third -- 32 percent -- said it was headed in the right direction. Six percent said they had mixed feelings and 3 percent said they weren't sure.
The WSJ/NBC poll indicated significant support for Obama's legislative agenda, including calls for stricter gun controls and plans to overhaul U.S. immigration laws and raise the minimum wage.
Overall, 50 percent approved Obama's job performance, 45 percent disapproved and 5 percent said they weren't sure. This is down from January's 52 percent approval, 44 percent disapproval and 4 percent not sure.
By a more than 2-to-1 margin, poll participants said Obama was doing more than Republicans to unify the country in a bipartisan way.
About 48 percent said they saw this of Obama, compared with 22 percent who said they saw this of Republicans and 37 percent who said the same of the Democratic Party.
The survey found 29 percent of those polled said they agreed with what Republicans are proposing in Congress. This compared with 40 percent who said they agreed with the Democrats' plans and 45 percent who agreed with Obama's proposals.
About 57 percent said they disagreed with what congressional Republicans are proposing, the highest level in Journal polling dating from 1995. The portion that said they disagreed with what congressional Democrats and Obama are proposing was 46 percent.
The newspaper and TV network's nationwide poll of 1,000 adults was conducted Thursday through Sunday by Bill McInturff of Public Opinion Strategies and Fred Yang of Peter D. Hart Research Associates. Its margin of error is 3.1 percentage points.
The Gallup poll was conducted of 1,017 adults Monday and Tuesday, and has a margin of error of 4 percentage points.