The CNN/Opinion Research Corporation survey, released Monday, also indicates that President Barack Obama's approval rating has experienced a similar six-point rise.
According to the poll, 42 percent of Americans, based on what they've read or heard about the bill, support Senate Democrat's legislation. That's up from 36 percent in a poll conducted December 2-3. Nonetheless, a majority of people questioned in the survey, 56 percent, oppose the bill.
The CNN/Opinion Research Corporation poll was conducted Wednesday through Sunday, as Senate Democrats were negotiating a final health care bill, but before a crucial party-line vote early Monday morning to end debate, a huge hurdle to eventual passage of the legislation that the Democrats successfully were able to jump.
"Virtually all the increase in support for the Senate health care bill has come from Democrats, with a 10-point increase since early December," says CNN Polling Director Keating Holland. "Support is also up 10 points among younger Americans, compared to only two points among people 50 and older."
The survey also indicates the public's divided on whether the Senate bill will help most Americans, with 38 percent saying if the bill becomes law things will change for the worse, 34 percent feeling that the bill will change things for the better and 26 percent saying things will not change.
But less than 1 in 4 think the bill will make their own health care coverage better, 15 points lower than the 37 percent who say their health care will get worse if the bill becomes law. Nearly 4 in 10 say there will be no change in their or their immediate family's coverage.
According the to poll, 54 percent of Americans approve of the job Obama's doing as president, up 6 points from early December, with 44 percent disapproving, down 6 points.
"Obama's approval rating is up ten points among younger Americans, but only two points among older Americans," Holland says. "Since the same pattern occurs in the figures for the Senate health care bill, it's possible that the two are related. Obama's support is also up mostly among liberals, to 81 percent."
But the survey also indicates Obama may not be living up to expectations. Nearly half of those polled, 48 percent, feeling that Obama's fallen short. The 48 percent who say the president's fallen short of their expectations is up 20 points from May.
"There is less confidence in Obama at the end of his first calendar year in office," says Holland. "In the spring, 64 percent thought his policies would succeed. That's down 12 points. And the number who say they want his policies to fail has doubled, to 22 percent, in that time."
The CNN/Opinion Research Corporation poll was conducted December 16-20, with 1,160 adult Americans questioned by phone. The survey's overall sampling error is plus or minus 3 percentage points.
Full results (pdf)
– CNN Deputy Political Director Paul Steinhauser contributed to this report
– Follow Paul Steinhauser on Twitter: @psteinhausercnn