President Trump meets Tuesday at the White House with congressional Republican leaders -- anattempt to jumpstart efforts on overhauling ObamaCare, tax reform and other parts of his domestic agenda slowed by the Russia investigations and Capitol Hills notoriously long legislative process.

"Big meeting today with Republican leadership concerning Tax Cuts and Healthcare, Trump tweeted Tuesday morning. We are all pushing hard - must get it right!"

Under pressure to get at least one legislative victory in his first term, Trump is in fact meeting with the lawmakers twice Tuesday.

He will meet in the afternoon with GOP leaders of the House and Senate, then host a working White House dinner for a handful of Republicans members, White House legislativedirector Marc Shortsaid Monday.

However, Senate Republicans have already quickened the pace on ObamaCare, after being urged last week by Treasury Secretary Steve Mnuchin to vote this summer to increase the federal debt ceiling.

Sources told Fox News on Monday that the GOP-led Senate now wants to vote on ObamaCare as soon as possible so members can devote July to the debt-ceiling debate and September to tax reform, with the intent of providing tax breaks to voters.

Senate Republican leaders emerged Monday from their regular weekly meeting with the surprise announcement that they have a draft bill on overhauling ObamaCare and that a vote could happen as early as July 4.

Texas Sen. John Cornyn, the chambers No. 2 Republican, was among the more cautious about the timeline, saying a vote would come sometime in July.

The ObamaCare push in the Senate follows the House last month passing its version, which congressional analysts say would end health-care coverage for an estimated 23 million Americans.

Senate Republicans have met privately for weeks on the issue and say they will have their own legislation. However, they realize that any plan that cuts the deficit by billions will also likely mean less coverage, particularly for those with pre-existing medical conditions.

Sen. Richard Burr, R-N.C., in fact said last week that a vote on ObamaCare by the end of the year was unlikely.

Short also acknowledged Monday that congressional investigations -- like the two on Capitol Hill on whether the Trump campaign colluded with Russia in the 2016 elections -- detracts from the presidents agenda.

But theres been lots of progress we're pleased about this spring, he added.

Trump, a former real estate magnate, complained last month about the slow pace of the Senate.

It's an archaic system, he told Fox News. It's really a bad thing for the country."

Short also said Monday that he doesnt expect legislation on tax reform until after Labor Day and that an infrastructure deal would come by the end of the year but the administration has no firm timeline.

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Trump tries to fire up tax reform, health care agenda amid turmoil - Fox News