WASHINGTON — Republicans in the House and Senate have reached an agreement in principle on their sweeping tax package that will slash individual and corporate rates, White House and GOP sources said Wednesday.

Once the details are ironed out, Republicans hope to have a vote in the Senate first, then the House, with the legislation done in Congress by next Wednesday, a White House official said. It can then be sent to President Donald Trump for his signature.

Two Republican sources familiar with the outlines of the deal confirmed to NBC News that the corporate tax rate would be cut to 21 percent, while the top tax rate for individuals would drop to 37 percent from 39.6 percent. The new rates would take effect next year. The bill also repeals Obamacare's individual mandate — overturning a key part of the health care law that requires individuals to buy insurance or pay a fine.

The deduction for state and local taxes would be capped at $10,000 and taxpayers would be able to chose to deduct their property or income taxes, source said.

The standard deduction would be doubled under the deal, to $12,000 for individuals and $24,000 for families.

Related: Déjà vu: GOP’s race to pass tax bill echoes 2010 Obamacare fight

Republicans senators leaving a GOP lunch told NBC News that the agreement would also set deductions for pass-through income at 20 percent.

Under the deal, the mortgage interest deduction would be allowed on loans up to $750,000, the sources said.

House Speaker Paul Ryan, R-Wis., told Fox News that the House and Senate bills were "very similar, and that it wasn’t difficult to reconcile the differences."

Related: Treasury Department releases analysis of GOP tax plan. It’s only one page long.

A tax deal would be Trump's first legislative achievement — nearly 11 months after he was sworn in.

In remarks at the White House, Trump called the tax bill "the biggest thing we've worked on" and declared it would be "bigger than anything ever done in this country" — even larger than President Ronald Reagan's massive tax cuts.

The president has long touted the tax effort as an economic stimulus and jobs creator and reiterated that the administration thinks "the economy has a long way to grow and it needs the tax cut. … It needs it desperately."

Related: Fed hikes interest rate for third time this year

Appearing alongside Hatch and Rep. Kevin Brady, R-Texas, chairman of the House Ways and Means Committee, Trump said Republicans were still "negotiating some final points," and pressed that it was "very important for us to have a vote next week."

He signaled an openness to a corporate rate of 21 percent — noting that it's at 35 percent right now, so any reduction would leave him "thrilled."

The president congratulated key House and Senate lawmakers who had lunch with him Wednesday for their efforts on tax reform, but stopped to wonder if maybe his excitement wasn't premature.

"We've been here so many times," Trump joked, his words recalling the stinging defeat Republicans suffered this year when they failed to repeal Obamacare. "Let's get the vote first."

Later, in a speech billed by White House officials as the president's final pitch for tax reform, Trump said Republicans were "so close" to passing tax reform.

Ever the reality show producer, Trump declared he had a "breaking news" announcement about the plan: "If Congress sends me a bill before Christmas, the IRS...has just confirmed Americans will see lower taxes and bigger paychecks beginning in February."

Trump relished the chance to not only tout the broad strokes of the tax plan on television, but also to allow several middle-class families, who were invited to join him at the White House, the chance to talk about how they would be impacted by the tax changes.

"Discuss your middle-class tax cut a little bit with the millions of people watching right now on television," Trump instructed one of the couples, who heaped praise and prayers on the president during short remarks.

With all 48 Democrats currently in the Senate (Democrats will pick up a seat after Doug Jones, newly elected in Alabama, is sworn in) likely united against the plan, Republicans can afford to lose only two GOP votes — and it remained unclear whether all Republican senators would be on board with the deal.

The chatter over a deal came just hours after Democratic Senate Minority Leader Chuck Schumer called on Republicans to "hit pause" on their tax bill until Jones takes his seat.

"It would be wrong for Senate Republicans to jam through this tax bill without giving the newly elected senator for Alabama the opportunity to cast his vote," Schumer said. "He won an election."

Related: Winners and losers in the Senate tax bill

Jones' stunning upset victory against GOP candidate Roy Moore Tuesday night shaved a once safe seat away from the Republicans' narrow majority in the Senate, decreasing it to 51 once Jones is seated, and potentially placing the tax plan in jeopardy.

"Will they have the strength and political foresight to start over or at least to modify their bill?" Schumer asked. "Or will they just bow ahead pretending not to hear the voices of the middle class crying about against this will?"

Schumer noted that Democrats faced a similar dilemma in 2010, when Republican Scott Brown beat Democrat Martha Coakley in a Massachusetts Senate special election, costing Democrats a key vote in the Senate as they were finalizing Obamacare.

"I am convinced now that no gamesmanship will be played by the other side with regard to future votes in the Senate," Sen. Mitch McConnell, R-Ky., said in 2010, when he was serving as the minority leader.

Then-Senate Majority Leader Harry Reid, D-Nev., said his party would not “rush into anything” and "wait until the new senator arrives" until they moved forward with health care.

"McConnell ought to do what he said ought to be done in 2010 and what we did in 2010 — delay until Doug Jones gets here and can cast a vote," Schumer said. "Plain and simple."