Yes. We have online access to thousands of newspapers, many with same day access to their articles, plus many historical archives of papers.
Start by searching the Journal Title Database for the paper in question. It will show what access we have by date and provider. Papers in Access World News will typically include same day articles. Papers in EBSCO and Gale will usually have a delay in loading the newest articles.
For information about databases providing access to newspapers and other new sources, visit our Newspapers and Current News Sources Guide.
If we don't subscribe to a newspaper where an article you're looking for was published, you can request the article through Interlibrary Loan, but you will need the precise date of publication, and ideally the section and page number too. You can use Discovery Search to try to find a complete citation (be sure to click the checkbox "Expand My Results" to search libraries worldwide) or try Google.