President Obama’s top aides met with Senate Republicans on Thursday as part of the White House’s ongoing effort to forge a deficit grand bargain.

Chief of staff Denis McDonough, deputy chief of staff Rob Nabors, National Economic Council Director Gene Sperling, and chief congressional liaison Miguel Rodriguez met with the Republicans, a source familiar with the meeting said. 

{mosads}Obama has held two dinners with Senate Republicans and this week hosted a bipartisan group of women senators at the White House for a third dinner.

He is seeking to find a coalition able to strike a budget deal ahead of a looming crisis over raising the debt ceiling this summer. The debt ceiling comes back into effect on May 19, forcing Treasury to start making moves to forestall a default. 

Obama’s 2014 budget contained significant concessions to Republicans in the form of lower Social Security benefits due to a change in the way inflation is measured and means testing for Medicare. So far, no Republican has embraced the more than $1 trillion in new taxes in the new Obama budget, however. 

The concessions won limited praise from Republicans, with some like Sen. Lindsey Graham (R-S.C.) saying they are willing to accept some new tax revenue in exchange for further cuts.

Senate Finance Committee Ranking Member Orrin Hatch (R-Utah) attended the meeting, aides said. In addition to discussing his ideas for Medicare and Medicaid, Hatch also brought up his desire for Obama to seek trade promotion authority in order to finalize the Transpacific Partnership agreement (TPA).

TPA would fast track any trade deal Obama signs, guaranteeing an up-or-down vote without amendments so long as certain conditions are met. Trade proponents say the bill is necessary since foreign leaders would be reluctant to strike a deal that Congress would then try to amend.

Sen. Lamar Alexander (R-Tenn.) said earlier this week that he thinks Obama’s outreach has a chance.

“I think there is a genuine effort by the president and the Democrats to see if there is some way that we can agree on at least a step toward fixing the debt. It may not be a grand bargain, but it could be a step toward getting the entitlement benefit structure on a better path over the long term,” he said.

“It is happening because the president has become directly involved. This is not like immigration where eight senators can produce a proposal. If there is a proposal, it will have to come from the president. I don’t blame him for not wanting to make it until he can count on some Republican support,” he said.

Sen. John Hoeven (R-N.D.) also attended the meeting with McDonough.

“I have talked to him a number of months … the objective is to get to entitlement reform and tax reform to get us to a $4 trillion deal,” he said.

“We are making progress from the standpoint of we are talking.  We shared concepts and ideas, talked about the president’s proposals,” Hoeven added.

But the North Dakota senator struck a note of caution, pointing out that there were still wide differences between the White House and Senate GOP.

“From our standpoint he has said he is willing to take on entitlements and that’s a positive but we still believe he raises taxes too much and spends too much. There’s clear points of disagreement,” he said.

Hoeven said that considering long-term entitlement reform could prove fruitful for efforts at an accord and that talks would continue.

This story was last updated at 4:07 p.m.