Republican lawmakers are concerned about how their tax bill is being viewed by the public and say they need to do a better job of selling it to middle-class and low-income voters.

A CBS News poll conducted last week found that 53 percent of people nationwide disapprove of the GOP tax bill and only 35 percent approve.

While support for the bill was strong among self-identified Republicans, according to the poll, 52 percent of independents and a whopping 84 percent of Democrats disapprove of the legislation.

Sen. Marco Rubio (R-Fla.) on Friday warned that the Republican Party cannot become identified with the "country club-big business image," citing a famous speech Ronald Reagan gave in 1977 using those same words.

While Speaker Paul Ryan (R-Wis.) is touting the projection that a median family of four in his home state would receive an average tax cut of $2,000 from the bill, some lawmakers worry about people who won't see any relief or who may even end up paying more.

Rubio and Sen. Mike Lee (R-Utah) tried to amend the Senate tax bill on the floor to provide more help to people on lower income rungs. Their proposal would have made the child tax credit refundable against payroll taxes

Twenty Republicans voted for the change, but it failed.

Rubio on Friday warned there are "going to be problems" if Senate and House negotiators working on the final legislation reduce the bill's child tax credit or increase the corporate rate without making the child tax credit refundable to help lower-income families.

"It makes a lot of sense in a tax-reform bill to provide some relief to those on the lower end of the income scale as well as the upper end," said Whit Ayres, a Republican pollster who does work for Rubio.

Ayres said Rubio is right that "it will help the overall perception of this bill if it's perceived of helping everyone who's working, not just those at the upper end of the income scale."

Another Republican senator, who commented on the condition of anonymity, said that "lowering the corporate rate is never popular."

"Forty-four percent of the country won't see anything and then they see headlines about a big corporate rate cut," said the lawmaker, explaining the weak public support for the bill.

Sen. Bob Corker (R-Tenn.), who was the only Republican to vote against the Senate tax bill, says he's concerned for different reasons.

He's worried the legislation will erode the GOP's credibility on fiscal responsibility - something that cost them dearly in the 2006 midterm elections, when Democrats captured control of the Senate and House.

Corker, the only Republican newly elected to the Senate in 2006, said fiscal issues were a top issue for Republican and independent voters that year.

"The Medicare Part D had been passed unpaid for and Republicans were viewed as spendthrifts," he said, referring to the prescription drug benefit legislation that was the signature domestic accomplishment of President George W. Bush's first term.

"My concern is that our nation continues to rack up huge debts and this is another step in that direction," Corker added.

While Republican lawmakers recognize the bill may not be popular, they argue that the corporate tax rate must be lowered to put the U.S. business environment on par with European and Asian competitors.

Some Republicans say the problem is they're not doing a good enough job explaining to voters how cutting the corporate tax rate can stimulate the entire economy.

"I think we have got to do a better job of communicating to America what's in this. This is hugely stimulative with regard to what's going to happen to the American worker," said Sen. David Perdue (R-Ga.), who is opposed to setting a corporate tax rate higher than 20 percent.

The bleak CBS poll numbers for the tax bill were in line with polls published earlier in the week by Quinnipiac and Gallup that showed 53 percent and 56 percent of the public, respectively, disapprove of the legislation.

The weak polling numbers prompted Republicans to play defense on Friday.

A senior administration official argued in a press call that the Quinnipiac and Gallup polls oversampled Democrats, which skewed the results to appear more unfavorable than actual public sentiment.

Jim McLaughlin, a Republican pollster, waved off the Quinnipiac poll as overly tilted toward Democrats.

"The Quinnipiac survey that came out earlier this week was 21 percent Republican. Are you kidding me? That's why [the polls] were so off in the election," he said.

He pointed to a survey of 1,000 likely voters nationwide conducted by his firm last month showing that 50 percent of respondents favored lowering the corporate tax rate to 20 percent, while only 37 percent opposed the move.

McLaughlin noted that there was strong public opposition to the Reagan administration's 1981 tax-cut package and that he went on to win reelection by a landslide in 1984, thanks in large part to a strong U.S. economy.

But he indicated there could be political problems in the near term if the legislation fails to deliver the promised economic results quickly.

"The Republicans got their heads handed to them in the off-year election, in 1982, we lost 26 House seats because they didn't make the tax cuts retroactive and people didn't think the economy was getting better quick enough."

The pending bill would not make tax cuts retroactive, but voters will see more money in their paychecks as soon as January, when employers adjust withholding rates for federal taxes.

Faced with the signs that the tax bill could be a political liability for GOP candidates in next year's midterm elections, Republicans are making some of the same arguments Democrats did in 2009 when they were trying to pass a massive health-care bill that did not poll well with voters.

Democrats argued at the time that while ObamaCare polled badly, voters supported its reforms when asked about them specifically. They said the legislation would become more popular over time.

Republicans are taking a similar tack now.

A senior administration official told reporters Friday that specific elements of the tax bill, such as the doubling of the standard deduction and the increasing of the child credit, have strong support.

Sen. Rob Portman (R-Ohio), who is crafting the final changes to the bill in a Senate-House conference committee, said the polling data about the bill can be misleading.

"The component parts are popular," he said. "It depends how you ask the corporate [rate] question. If you ask 'Do you think we should make American companies competitive by getting the rate below the [global] average?' the answer is yes."

Portman also disputed colleagues who say the bill doesn't do anything for people who don't pay income taxes.

"We've made the child tax credit a little more refundable and all the refundability stays in place," he said.

"Three million people, all told, are going to fall off the tax roles altogether," he said of people who now have an income tax liability but won't after the bill is signed into law.

More than 60 percent of households would see a tax cut of at least $100 in 2019 under the Senate GOP tax bill, but that percentage would drop in subsequent years, according to an analysis by the bipartisan Joint Committee on Taxation.

Still, Portman acknowledged the party has failed to clearly explain all the bill's benefits to the general public.

"We've got to figure out how to communicate better," he said.