Sen. Orrin HatchOrrin HatchOvernight Finance: US preps cases linking North Korea to Fed heist | GOP chair says Dodd-Frank a 2017 priority | Chamber pushes lawmakers on Trump's trade pick | Labor nominee faces Senate US Chamber urges quick vote on USTR nominee Lighthizer Live coverage: Day three of Supreme Court nominee hearing MORE (R-Utah) introduced an amendment Tuesday that would extend all the Bush-era tax cuts for another year.

Hatch wants to attach the amendment to the Small Business Jobs and Tax Relief Act (S. 2237).

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Hatch's amendment to the bill comes as Democrats conduct a coordinated effort to gain the advantage over Republicans on taxes. On Monday, President Obama called on Congress to extend the tax rates for incomes up to $250,000 a year. Later this month, Democrats also plan on voting for legislation that extends the Bush tax cuts for the income levels Obama wants for another year while allowing the tax cuts for earners making more than $250,000 annually to expire.

Hatch said that unless all the rates are extended, small businesses will suffer a "massive tax increase" when the cuts expire at the end of the year.

"So unless the Congress acts to prevent these massive tax increases, the vast majority of small businesses will be hit with a massive increase with a tax next year," Hatch said. "It is hard to conceive of a greater impediment to job creation. All of these tax increases and the economic uncertainty that they cause are going into the investment and hiring decisions of businessmen and women today."

The country's economic recovery is too fragile to not extend all the tax cuts, Hatch said.

"Here we are with a fragile recovery and a weak jobs market. President Obama seems content to sit idly by and allow this scheduled 4.5-trillion tax hike to occur," Hatch said. "I believe Congress needs to act now to prevent this tax hike on America's families and job creators."

Hatch's amendment falls in line with Republican objections to Obama's desire to extend some but not all of the tax cuts. Earlier on Tuesday, Senate Minority Leader Mitch McConnellMitch McConnellOvernight Healthcare: High drama for ObamaCare vote | Freedom Caucus chair 'optimistic' about deal | Trump woos right High drama for ObamaCare vote Senate nixes Obama-era workplace safety rule MORE (R-Ky.) said that the tax cuts for all income levels should be extended. House Speaker John BoehnerJohn BoehnerFreedom Caucus leader: Despite changes, healthcare bill doesn't have the votes Debt ceiling returns, creating new headache for GOP Letters: Congress, raise the debt limit now MORE (R-Ohio) also wants all the tax cuts extended.

"If we allow this tax relief to expire as scheduled at the end of the year, almost every federal income tax payer in America will see an increase in their rates," Hatch continued. "Our economy simply cannot afford to take on such a fiscal shock."

—This story was updated at 6:28 p.m.

Read the amendment below:

Hatch Amendment