The poll found that Democrats (49 percent) were more likely to prefer one-party government than Republicans (36 percent) or independents (28 percent).
"There may be several reasons for this," Gallup said. "Democrats currently control the presidency and many Democrats may be frustrated that President Barack Obama cannot enact his legislative agenda without the help of a sympathetic Congress. Also, Democrats are more likely than Republicans to express faith in the federal government's ability to handle domestic problems."
The poll found that Democrats' preference for one-party government rose significantly in 2012 -- to 49 percent from 35 percent last year. Independents' preference for one-party government was up 7 points from last year, and there was no significant change in Republicans' preference, year-to-year.
The implications, according to Gallup: As the 2012 election approaches, Americans may be somewhat less open to ballot-splitting than in prior years.
The pollster also noted that support for one-party government typically increases in presidential election years, and the surge in Democrats' preferences may reflect their growing enthusiasm about the election more broadly.
In 2004, when President Bush and a Republican Congress stood for re-election, Republican voters preferred unified over divided government, 59-18 percent. Democrats in contrast preferred divided government (42 percent) to one-party government (37 percent).
Here's how Gallup framed the question: Better for the Country to Have the Presidency and Congress Controlled by the Same Party, Controlled by Different Parties, or Does It Make No Difference Either Way?
Gallup's annual Governance Survey is based on telephone interviews conducted September 6-9, 2012 on a random sample of 1,017 adults living in all 50 U.S. states and the District of Columbia. The polls has a margin of error of plus or minus 4 points.
With the help of a Democrat-led House and Senate, President Obama was able to fundamentally change the health insurance business by signing the health care bill into law in March 2010.
But it's been legislative gridlock since Republicans took back the House in the 2010 midterm election.
In October 2011, President Obama announced his "We Can't Wait" campaign, insisting, "We can't wait for an increasingly dysfunctional Congress to do its job. Where they won’t act, I will."
Since then, Obama has bypassed Congress in a number of areas, including immigration, education, and energy policy.