NEW YORK (TheStreet) -- Stocks gave up some of their gains on Tuesday, as a default on Greece's debt payment due to the International Monetary Fund looks unavoidable.  

The S&P 500 rose 0.38%, the Dow Jones Industrial Average added 0.34% and the Nasdaq increased 0.49%, following a major selloff in all the indices on Monday. The Dow lost 350 points on Monday and entered negative territory for the year.

While no deal is in place for Greece's debt and a default looks likely, Greek Finance Minister Yanis Varoufakis told Reuters he is hopeful a last-minute agreement will be made.

The debt-laden country has a $1.7 billion payment due to the International Monetary Fund at midnight Tuesday Athens time and reports are that Greece won't make the payment.

Greece announced over the weekend that it will hold a referendum on July 5 to allow citizens to decide if the country should remain in the 19-country eurozone. A "Grexit" would mean a return to Greece's old drachma currency.

Investors in Europe weren't optimistic about a Greek resolution, with London's FTSE 100 down 1.06%, Frankfurt's DAX down 0.78% and Paris's CAC 40 to the downside by 0.98%. The euro lost 0.53% against the dollar.

"Unless there is a last ditch agreement [Tuesday] between Athens and the creditors to extend the bailout program by five months (with partial debt relief or a commitment hereto), [Monday's] recovery in euro assets is likely to prove fleeting," wrote Societe Generale's Kenneth Broux in a note. "The probability of a deal happening is low and means Greece will fall in arrears with the IMF today if it does not honor the repayment."

Greece isn't the only country with a debt crisis on its hands. Puerto Rico's Gov. Alejandro Garcia Padilla said on Sunday that the island's $72 billion in debt is "not payable," posing risks for the U.S. municipal bond market. Though the White House said a bailout for Puerto Rico was not being considered.

The S&P/Case-Shiller Home Price Index, which tracks home prices in 20 metropolitan cities, rose 0.3% in April, falling short of estimates of 0.8%. The June reading on consumer confidence from the Conference Board's Consumer Confidence Index reached 101.4, reaching a critical triple-digit level that eclipsed estimates of 97.4.

Oil prices saw a significant increase of over 1% to $58.97 a barrel. 

Apple's (AAPL) streaming music service begins on Tuesday for $9.99 a month, following a 90-day free trial. The service will include music from Taylor Swift, who removed her songs from competitor streaming service Spotify. Apple's service is also set to compete with Pandora (P).

Willis (WSH) and Towers Watson (TW) have agreed to merge in a deal valued at roughly $18 billion. The new company will be called Willis Towers Watson and will have 39,000 employees across 120 nations. Willis shares rose 5%, while Towers Watson fell 2.3%. 

Shares of Apollo Education (APOL) slumped 13.7% after the company reported third-quarter earnings per share of 53 cents, on an adjusted basis, down from 78 cents a year earlier.

Celgene (CELG) shares were trading lower after the company said it will spend $1 billion over the next decade in a partnership with Juno Therapeutics (JUNO) to develop treatments for various immune system diseases.

ConAgra Foods (CAG) reported adjusted quarterly earnings per share of 59 cents, in line with estimates. Shares fell 1.2% after the company announced that it expects to exit its private label operations.

AOL (AOL) will take control of Microsoft's (MSFT) Web display advertising operations. AOL was recently acquired by Verizon (VZ). Shares of Microsoft fell 0.6%.

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