Senate Democrats would raise nearly $1 trillion in new taxes under a budget proposal they laid out for President Obama while lunching with him in the U.S. Capitol on Tuesday.

The president is making the rounds in the Capitol to help facilitate talks on a budget deal, which is set to consume lawmakers in the coming months as they work to strike a "grand bargain" on reducing the nation's debt and deficit.

"He is very supportive of the path we are moving down," Sen. Patty Murray, D-Wash., said after the lunch.

Murray, who chairs the Senate budget panel, will unveil a budget plan Wednesday that would use $975 billion in tax increases and $975 billion in spending cuts to achieve $1.85 trillion in deficit reduction, according to those familiar with the plan.

The proposal would also include $100 billion in new stimulus spending on infrastructure and other programs aimed at promoting job growth.

Murray uses tax increases and other spending cuts to stop the $1.2 trillion sequester that kicked in on March 1, according to those who have seen the plan.

Murray's plan is at odds with the House Republican budget unveiled Tuesday, which cuts $5.7 trillion in spending and does not raise taxes or add new spending.

Obama's rare visit to Congress culminated in a meeting with key Democrats for about an hour and 20 minutes about budget matters and the nation's climbing debt and deficit.

The president answered questions from more than a dozen Democratic lawmakers about a wide range of topics, including his willingness to cut entitlement spending in order to strike a deal with Republicans on shrinking the deficit.

It was the first of four meetings Obama will hold this week with lawmakers in both chambers. He will meet with the House GOP on Wednesday afternoon and then heads back to the Senate to lunch on lobster with Republicans on Thursday. He'll also meet with House Democrats on Thursday.

According to Sen. Mary Landrieu, D-La., who attended the Tuesday lunch, Obama "is completely in line" with Murray's budget and he stressed the importance of "sticking together" as a party when it comes to budget matters.

But some liberal Democrats are wary of Obama negotiating with Republicans on entitlement reforms that could include lowering benefits for future recipients of Medicare and Medicaid and Social Security.

In past spending negotiations, Republicans have pointed out, Obama has signaled a willingness to slow the growth of cost-of-living adjustments to Social Security benefits in exchange for new taxes.

Republicans, Senate Majority Leader Harry Reid, D-Nev., said after the lunch, "take these things that are talked about in abstract and say that's what we agreed to. We haven't agreed to any of that."

Sen. Claire McCaskill, D-Mo., admitted the Democrats had some differences with Obama on entitlements but were working them out.

"We are trying to stay united," she said after the meeting.

Murray's budget does not call for entitlement reform, and it is not clear yet whether Obama's budget, which is scheduled for release next month, will propose any changes to entitlement spending.

Sen. Carl Levin, D-Mich., suggested Obama wants the Democrats to understand they would have to give up something if the two sides are ever going to strike a deal.

"He thinks it's very important that we solve these problems together," Levin said, "that working together with Republicans for a grand bargain is critically important, and compromise is essential."